In GaN-based green light-emitting diodes（LEDs） with and without Mg-preflow before the growth of p-Al GaN electron blocking layer（EBL） are investigated experimentally.A higher Mg doping concentration is achieved in...In GaN-based green light-emitting diodes（LEDs） with and without Mg-preflow before the growth of p-Al GaN electron blocking layer（EBL） are investigated experimentally.A higher Mg doping concentration is achieved in the EBL after Mg-preflow treatment,effectively alleviating the commonly observed efficiency collapse and electrons overflowing at cryogenic temperatures.However,unexpected decline in quantum efficiency is observed after Mg-preflow treatment at room temperature.Our conclusions are drawn such that the efficiency decline is probably the result of different emission positions.Higher Mg doping concentration in the EBL after Mg-preflow treatment will make it easier for a hole to be injected into multiple quantum wells with emission closer to pGaN side through the（8-plane rather than the V-shape pits,which is not favorable to luminous efficiency due to the preferred occurrence of accumulated strain relaxation and structural defects in upper QWs closer to p-GaN.Within this framework,apparently disparate experimental observations regarding electroluminescence properties,in this work,are well reconciled.展开更多
This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetr...This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.展开更多
Based on the limit analysis upper bound method, a new mechanism of soil slope failure has been proposed which was consisted of plastic shear zone and rigid block zone. The different zones interface were regarded as di...Based on the limit analysis upper bound method, a new mechanism of soil slope failure has been proposed which was consisted of plastic shear zone and rigid block zone. The different zones interface were regarded as discontinuity lines. Two sliding blocks of the slope were also incorporated horizontal seismic force and vertical gravity force. The velocities and forces were analyzed in two blocks, and the expression of velocity discontinuities was derived according to the principle of incompressibility. The external force done work for the blocks and the internal energy dissipated of the plastic shear zone and the velocity discontinuous were solved.The stability ratios were derived for the height of two-level slope with different rates to involve seismic and no seismic. The present stability ratios were compared to the previous study, which showed the superiority of the mechanism and the rationality of the analysis. The critical height of the slope can provide a theoretical basis for slope support and design.展开更多
The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidi...The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidiagonalization methods derived from a symmetric augmented multiple linear systems and make a comparison with the block GMRES and block biconjugate gradient methods.展开更多
This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the nume...This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the numerical processes that satisfy an important asymptotic stability condition related to the class of test problems y′(t)=ay(t)+by(t-τ) with a,b∈C, Re(a)<-|b| and τ>0. We prove that the block θ method is GP stable if and only if the method is A stable for ordinary differential equations. Furthermore, it is proved that the P and GP stability are equivalent for the block θ method.展开更多
In this paper, a block method with one hybrid point for solving Jerk equations is presented. The hybrid point is chosen to optimize the local truncation errors of the main formulas for the solution and the derivative ...In this paper, a block method with one hybrid point for solving Jerk equations is presented. The hybrid point is chosen to optimize the local truncation errors of the main formulas for the solution and the derivative at the end of the block. Analysis of the method is discussed, and some numerical examples show that the proposed method is efficient and accurate.展开更多
Historical and cultural blocks are witnesses of history and inheritors of culture. As one of the main spaces for outdoor interaction in historical and cultural blocks, the improvement of its vitality is of great signi...Historical and cultural blocks are witnesses of history and inheritors of culture. As one of the main spaces for outdoor interaction in historical and cultural blocks, the improvement of its vitality is of great significance for the improvement of residential environment and the better inheritance of history and culture. Taking Daopashi Street in Anqing City as an example, an evaluation model of landscape spatial vitality of historical and cultural blocks was constructed from three aspects of viewing function, store status and service facilities, and analytic hierarchy process was used to determine the index weight and vaguely evaluate the landscape spatial vitality of historical and cultural blocks. The results show that through the comparison of weight, architectural style(0.317), the practicability of service facilities(0.168) and plant landscape(0.165) had a significant impact on the landscape spatial vitality of historical and cultural blocks,and the landscape spatial vitality of historical and cultural blocks in Daopashi Street in Anqing City was at a good level.展开更多
Text extraction is an important initial step in digitizing the historical documents. In this paper, we present a text extraction method for historical Tibetan document images based on block projections. The task of te...Text extraction is an important initial step in digitizing the historical documents. In this paper, we present a text extraction method for historical Tibetan document images based on block projections. The task of text extraction is considered as text area detection and location problem. The images are divided equally into blocks and the blocks are filtered by the information of the categories of connected components and corner point density. By analyzing the filtered blocks' projections, the approximate text areas can be located, and the text regions are extracted. Experiments on the dataset of historical Tibetan documents demonstrate the effectiveness of the proposed method.展开更多
Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number o...Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.展开更多
In [1], a class of multiderivative block methods (MDBM) was studied for the numerical solutions of stiff ordinary differential equations. This paper is aimed at solving the problem proposed in [1] that what conditions...In [1], a class of multiderivative block methods (MDBM) was studied for the numerical solutions of stiff ordinary differential equations. This paper is aimed at solving the problem proposed in [1] that what conditions should be fulfilled for MDBMs in order to guarantee the A-stabilities. The explicit expressions of the polynomialsP(h) and Q(h) in the stability functions h(h)=P(h)/Q(h)are given. Furthermore, we prove P(-h)-Q(h). With the aid of symbolic computations and the expressions of diagonal Fade approximations, we obtained the biggest block size k of the A-stable MDBM for any given l (the order of the highest derivatives used in MDBM,l>1)展开更多
Iterative methods that take advantage of efficient block operations and block communications are popular research topics in parallel computation. These methods are especially important on Massively Parallel Processors...Iterative methods that take advantage of efficient block operations and block communications are popular research topics in parallel computation. These methods are especially important on Massively Parallel Processors (MPP). This paper presents a block variant of the GMRES method for solving general unsymmetric linear systems. It is shown that the new algorithm with block size s, denoted by BVGMRES(s,m), is theoretically equivalent to the GMRES(s. m) method. The numerical results show that this algorithm can be more efficient than the standard GMRES method on a cache based single CPU computer with optimized BLAS kernels. Furthermore, the gain in efficiency is more significant on MPPs due to both efficient block operations and efficient block data communications. Our numerical results also show that in comparison to the standard GMRES method, the more PEs that are used on an MPP, the more efficient the BVGMRES(s,m) algorithm is.展开更多
Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwat...Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwater is solved using the finite-depth Green function and boundary element method, in which the Green function is solved by integral method. The Response-Amplitude Operator(RAO) of wave pressure is acquired according to the Longuet-Higgins' wave model and the linear Bernoulli equation. Furthermore, the wave pressure's response spectrum is calculated according to the wave spectrum by discretizing the frequency domain. The wave pressure's characteristic value corresponding to certain cumulative probability is determined according to the Rayleigh distribution of wave heights. The numerical results and field test results are compared, which indicates that the wave pressure calculated in random seas agrees with that of field measurements. It is found that the bigger angle between legs will cause the bigger pressure response, while the increase in leg length does not influence the pressure significantly. The pressure at the side of head sea is larger than that of back waves. When the incident wave angle changes from 0? to 90?, the pressure at the side of back waves decreases clearly, while at the side of head sea, the situation is more complicated and there seems no obvious tendency. The concentration of wave energy around low frequency(long wavelength) will induce bigger wave pressure, and more attention should be paid to this situation for the structure safety.展开更多
Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical res...Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency.Hybrid block methods for instance are specifically used in numerical integration of initial value problems.In this paper,an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations(ODEs).In deriving themethod,the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval.Furthermore,the convergence properties along with the region of stability of the method were examined.It was concluded that the newly derived method is convergent,consistent,and zero-stable.The method was also found to be A-stable implying that it covers the whole of the left/negative half plane.From the numerical computations of absolute errors carried out using the newly derived method,it was found that the method performed better than the ones with which we compared our results with.Themethod also showed its superiority over the existing methods in terms of stability and convergence.展开更多
Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ord...Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ordinary differential equations(ODEs)usually found in most applied problems.This study aims to develop a new numerical method,namely the high order variable step variable order block backward differentiation formula(VSVOHOBBDF)for the main purpose of approximating the solutions of third order ODEs.The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code.The order of the proposed method was then discussed in detail.The advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions effectively.In order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB,particularly ode15s and ode23s,a numerical experiment was conducted on a set of stiff problems.The numerical results prove that for this particular set of problem,the use of the proposed method is more efficient than the comparable methods.VSVO-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs.展开更多
In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a sy...In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a system of nonlinear Volterra integral equations. Runge-Kutta method (RKM) and Bolck by block method (BBM) are used to solve the system of nonlinear Volterra integral equations of the second kind (SNVIEs) with continuous kernel. The error in each case is calculated.展开更多
The adaptive simpler block GMRES method was investigated by Zhong et al.(J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this p...The adaptive simpler block GMRES method was investigated by Zhong et al.(J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this paper, the new upper bound for the condition number is investigated. Numerical tests show that the new upper bound is tighter.展开更多
In this paper, we developed a new continuous block method using the approach of collocation of the differential system and interpolation of the power series approximate solution. A constant step length within a half s...In this paper, we developed a new continuous block method using the approach of collocation of the differential system and interpolation of the power series approximate solution. A constant step length within a half step interval of integration was adopted. We evaluated at grid and off grid points to get a continuous linear multistep method. The continuous linear multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent and zero stable hence convergent. The new method was tested on real life problems namely: SIR model, Growth model and Mixture Model. The results were found to compete favorably with the existing methods in terms of accuracy and error bound.展开更多
In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evalua...In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model.展开更多
Many applications require the solution of large un-symmetric linear systems with multiple right-hand sides.Instead of applying an iterative method to each of these systems individually,it is often more efficient to us...Many applications require the solution of large un-symmetric linear systems with multiple right-hand sides.Instead of applying an iterative method to each of these systems individually,it is often more efficient to use a block version of the method that generates iterates for all the systems simultaneously.This paper proposes a new adaptive block QMR version based on the incomplete or-thogomalization method(IOM(q))for solving large multi-ple nusymmetric linear systems.How to incorporate de-flation to drop comverged linear systems,and how to delete linearly and almost liearly dependent vectors in the underlying block Krylov sequences are discussed.Nu-merical experiments show that the new adaptive block method has better practical performance and less compu-tational cost and CPU time than block GMRES and other proposed methods for the solution of systems with multi- ple right-hand sides.展开更多
基金Supported by the National Key R&D Program of China under Grant Nos 2016YFB0400600 and 2016YFB0400601the State Key Program of the National Natural Science of China under Grant No 61334001+2 种基金the Key R&D Program of Jiangxi Province under Grant No 20165ABC28007the Natural Science Foundation of Jiangxi Province under Grant No 20151BAB207053the National Natural Science Foundation of China under Grant No 21405076
文摘In GaN-based green light-emitting diodes（LEDs） with and without Mg-preflow before the growth of p-Al GaN electron blocking layer（EBL） are investigated experimentally.A higher Mg doping concentration is achieved in the EBL after Mg-preflow treatment,effectively alleviating the commonly observed efficiency collapse and electrons overflowing at cryogenic temperatures.However,unexpected decline in quantum efficiency is observed after Mg-preflow treatment at room temperature.Our conclusions are drawn such that the efficiency decline is probably the result of different emission positions.Higher Mg doping concentration in the EBL after Mg-preflow treatment will make it easier for a hole to be injected into multiple quantum wells with emission closer to pGaN side through the（8-plane rather than the V-shape pits,which is not favorable to luminous efficiency due to the preferred occurrence of accumulated strain relaxation and structural defects in upper QWs closer to p-GaN.Within this framework,apparently disparate experimental observations regarding electroluminescence properties,in this work,are well reconciled.
基金National Natural Science Foundation of China Under Grant No.51278382
文摘This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.
基金the National Natural Science Foundation of China(No.51478444,51574115 and 51774121)
文摘Based on the limit analysis upper bound method, a new mechanism of soil slope failure has been proposed which was consisted of plastic shear zone and rigid block zone. The different zones interface were regarded as discontinuity lines. Two sliding blocks of the slope were also incorporated horizontal seismic force and vertical gravity force. The velocities and forces were analyzed in two blocks, and the expression of velocity discontinuities was derived according to the principle of incompressibility. The external force done work for the blocks and the internal energy dissipated of the plastic shear zone and the velocity discontinuous were solved.The stability ratios were derived for the height of two-level slope with different rates to involve seismic and no seismic. The present stability ratios were compared to the previous study, which showed the superiority of the mechanism and the rationality of the analysis. The critical height of the slope can provide a theoretical basis for slope support and design.
基金The research of this author was supported by the National Natural Science Foundation of China,the JiangsuProvince Natural Science Foundation,the Jiangsu Province"333Engineering" Foundation and the Jiangsu Province"Qinglan Engineering" Foundation
文摘The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidiagonalization methods derived from a symmetric augmented multiple linear systems and make a comparison with the block GMRES and block biconjugate gradient methods.
文摘This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the numerical processes that satisfy an important asymptotic stability condition related to the class of test problems y′(t)=ay(t)+by(t-τ) with a,b∈C, Re(a)<-|b| and τ>0. We prove that the block θ method is GP stable if and only if the method is A stable for ordinary differential equations. Furthermore, it is proved that the P and GP stability are equivalent for the block θ method.
文摘In this paper, a block method with one hybrid point for solving Jerk equations is presented. The hybrid point is chosen to optimize the local truncation errors of the main formulas for the solution and the derivative at the end of the block. Analysis of the method is discussed, and some numerical examples show that the proposed method is efficient and accurate.
基金the Research on the Application of the Perception Teaching of“Graphics”in Architectural Design Course(JZ213702)Landscape Architecture Stracture(JZ213704)+1 种基金Research on the Teaching of Architectural Design Course for Urban and Rural Planning Major with the concept of“Local Design”(JZ223706)Anhui Provincial Key Laboratory of Huizhou Architecture Open Subjects Funding Project(HPJZ-2020-03).
文摘Historical and cultural blocks are witnesses of history and inheritors of culture. As one of the main spaces for outdoor interaction in historical and cultural blocks, the improvement of its vitality is of great significance for the improvement of residential environment and the better inheritance of history and culture. Taking Daopashi Street in Anqing City as an example, an evaluation model of landscape spatial vitality of historical and cultural blocks was constructed from three aspects of viewing function, store status and service facilities, and analytic hierarchy process was used to determine the index weight and vaguely evaluate the landscape spatial vitality of historical and cultural blocks. The results show that through the comparison of weight, architectural style(0.317), the practicability of service facilities(0.168) and plant landscape(0.165) had a significant impact on the landscape spatial vitality of historical and cultural blocks,and the landscape spatial vitality of historical and cultural blocks in Daopashi Street in Anqing City was at a good level.
基金supported by the Innovation Platform Construction of Qinghai Province(No.2016-ZJ-Y04)the Basic Research Program of Qinghai Province(No.2016-ZJ-740)
文摘Text extraction is an important initial step in digitizing the historical documents. In this paper, we present a text extraction method for historical Tibetan document images based on block projections. The task of text extraction is considered as text area detection and location problem. The images are divided equally into blocks and the blocks are filtered by the information of the categories of connected components and corner point density. By analyzing the filtered blocks' projections, the approximate text areas can be located, and the text regions are extracted. Experiments on the dataset of historical Tibetan documents demonstrate the effectiveness of the proposed method.
基金The project supported by the National Natural Science Foundation of China
文摘Based on elementary group theory, the block pivot methods for solving two-dimensional elastic frictional contact problems are presented in this paper. It is proved that the algorithms converge within a finite number of steps when the friction coefficient is ''relative small''. Unlike most mathematical programming methods for contact problems, the block pivot methods permit multiple exchanges of basic and nonbasic variables.
文摘In [1], a class of multiderivative block methods (MDBM) was studied for the numerical solutions of stiff ordinary differential equations. This paper is aimed at solving the problem proposed in [1] that what conditions should be fulfilled for MDBMs in order to guarantee the A-stabilities. The explicit expressions of the polynomialsP(h) and Q(h) in the stability functions h(h)=P(h)/Q(h)are given. Furthermore, we prove P(-h)-Q(h). With the aid of symbolic computations and the expressions of diagonal Fade approximations, we obtained the biggest block size k of the A-stable MDBM for any given l (the order of the highest derivatives used in MDBM,l>1)
文摘Iterative methods that take advantage of efficient block operations and block communications are popular research topics in parallel computation. These methods are especially important on Massively Parallel Processors (MPP). This paper presents a block variant of the GMRES method for solving general unsymmetric linear systems. It is shown that the new algorithm with block size s, denoted by BVGMRES(s,m), is theoretically equivalent to the GMRES(s. m) method. The numerical results show that this algorithm can be more efficient than the standard GMRES method on a cache based single CPU computer with optimized BLAS kernels. Furthermore, the gain in efficiency is more significant on MPPs due to both efficient block operations and efficient block data communications. Our numerical results also show that in comparison to the standard GMRES method, the more PEs that are used on an MPP, the more efficient the BVGMRES(s,m) algorithm is.
基金supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant no.51021004)the Research Fund of State Key Laboratory in Ocean Engineering of Shanghai Jiaotong University(Grant no.1104)the Scientific Research Foundation of Civil Aviation University of China(Grant no.09QD08X)
文摘Wave pressure on the wet surface of a V-shaped floating breakwater in random seas is investigated. Considering the diffraction effect, the unit velocity potential caused by the single regular waves around the breakwater is solved using the finite-depth Green function and boundary element method, in which the Green function is solved by integral method. The Response-Amplitude Operator(RAO) of wave pressure is acquired according to the Longuet-Higgins' wave model and the linear Bernoulli equation. Furthermore, the wave pressure's response spectrum is calculated according to the wave spectrum by discretizing the frequency domain. The wave pressure's characteristic value corresponding to certain cumulative probability is determined according to the Rayleigh distribution of wave heights. The numerical results and field test results are compared, which indicates that the wave pressure calculated in random seas agrees with that of field measurements. It is found that the bigger angle between legs will cause the bigger pressure response, while the increase in leg length does not influence the pressure significantly. The pressure at the side of head sea is larger than that of back waves. When the incident wave angle changes from 0? to 90?, the pressure at the side of back waves decreases clearly, while at the side of head sea, the situation is more complicated and there seems no obvious tendency. The concentration of wave energy around low frequency(long wavelength) will induce bigger wave pressure, and more attention should be paid to this situation for the structure safety.
基金This research was funded by Fundamental Research Grant Scheme(FRGS)under the Ministry of Higher Education Malaysia,grant number with project ref:FRGS/1/2019/STG06/UTP/03/2.
文摘Multistep integration methods are being extensively used in the simulations of high dimensional systems due to their lower computational cost.The block methods were developed with the intent of obtaining numerical results on numerous points at a time and improving computational efficiency.Hybrid block methods for instance are specifically used in numerical integration of initial value problems.In this paper,an optimized hybrid block Adams block method is designed for the solutions of linear and nonlinear first-order initial value problems in ordinary differential equations(ODEs).In deriving themethod,the Lagrange interpolation polynomial was employed based on some data points to replace the differential equation function and it was integrated over a specified interval.Furthermore,the convergence properties along with the region of stability of the method were examined.It was concluded that the newly derived method is convergent,consistent,and zero-stable.The method was also found to be A-stable implying that it covers the whole of the left/negative half plane.From the numerical computations of absolute errors carried out using the newly derived method,it was found that the method performed better than the ones with which we compared our results with.Themethod also showed its superiority over the existing methods in terms of stability and convergence.
基金funded by Fundamental Research Grant Scheme Universiti Sains Malaysia,Grant No.203/PJJAUH/6711688 received by S.A.M.Yatim.Url at http://www.research.usm.my/default.asp?tag=3&f=1&k=1.
文摘Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered stiff.Certain implicit methods,however,are capable of solving stiff ordinary differential equations(ODEs)usually found in most applied problems.This study aims to develop a new numerical method,namely the high order variable step variable order block backward differentiation formula(VSVOHOBBDF)for the main purpose of approximating the solutions of third order ODEs.The computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single code.The order of the proposed method was then discussed in detail.The advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions effectively.In order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB,particularly ode15s and ode23s,a numerical experiment was conducted on a set of stiff problems.The numerical results prove that for this particular set of problem,the use of the proposed method is more efficient than the comparable methods.VSVO-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs.
文摘In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a system of nonlinear Volterra integral equations. Runge-Kutta method (RKM) and Bolck by block method (BBM) are used to solve the system of nonlinear Volterra integral equations of the second kind (SNVIEs) with continuous kernel. The error in each case is calculated.
基金This work was supported by the National Natural Science Foundation of China(11701320)the Shandong Provincial Natural Science Foundation of China(ZR2016AM04).
文摘The adaptive simpler block GMRES method was investigated by Zhong et al.(J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this paper, the new upper bound for the condition number is investigated. Numerical tests show that the new upper bound is tighter.
文摘In this paper, we developed a new continuous block method using the approach of collocation of the differential system and interpolation of the power series approximate solution. A constant step length within a half step interval of integration was adopted. We evaluated at grid and off grid points to get a continuous linear multistep method. The continuous linear multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent and zero stable hence convergent. The new method was tested on real life problems namely: SIR model, Growth model and Mixture Model. The results were found to compete favorably with the existing methods in terms of accuracy and error bound.
文摘In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model.
文摘Many applications require the solution of large un-symmetric linear systems with multiple right-hand sides.Instead of applying an iterative method to each of these systems individually,it is often more efficient to use a block version of the method that generates iterates for all the systems simultaneously.This paper proposes a new adaptive block QMR version based on the incomplete or-thogomalization method(IOM(q))for solving large multi-ple nusymmetric linear systems.How to incorporate de-flation to drop comverged linear systems,and how to delete linearly and almost liearly dependent vectors in the underlying block Krylov sequences are discussed.Nu-merical experiments show that the new adaptive block method has better practical performance and less compu-tational cost and CPU time than block GMRES and other proposed methods for the solution of systems with multi- ple right-hand sides.
