Time synchronization is a prerequisite for ensuring determinism in time-sensitive networking(TSN).While time synchronization errors cannot be overlooked,pursuing minimal time errors may incur unnecessary costs.Using c...Time synchronization is a prerequisite for ensuring determinism in time-sensitive networking(TSN).While time synchronization errors cannot be overlooked,pursuing minimal time errors may incur unnecessary costs.Using complex network theory,this study proposes a hierarchy for TSN and introduces the concept of bounded time error.A coupling model between traffic scheduling and time synchronization is established,deriving functional relationships among end-to-end delay,delay jitter,gate window,and time error.These relationships illustrate that time errors can trigger jumps in delay and delay jitter.To evaluate different time errors impact on traffic scheduling performance,an end-to-end transmission experiment scheme is designed,along with the construction of a TSN test platform implementing two representative cases.Case A is a closed TSN domain scenario with pure TSN switches emulating closed factory floor network.Case B depicts remote factory interconnection where TSN domains link via non-TSN domains composed of OpenFlow switches.Results from Case A show that delay and delay jitter on a single node are most significantly affected by time errors,up to one gating cycle.End-to-end delay jitter tends to increase with the number of hops.When the ratio of time error bound to window exceeds 10%,the number of schedulable traffic flows decreases rapidly.Case B reveals that when time error is below 1μs,the number of schedulable traffic flows begins to increase significantly,approaching full schedulability at errors below 0.6μs.展开更多
This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administratio...This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administration.The analysis reveals systematic improvements in both track and intensity forecasts over the decade,with distinct error characteristics observed across various forecast parameters.Track forecast errors have steadily decreased,particularly for longer lead times,while error magnitudes have increased with longer forecast lead times.Intensity forecasts show similar progressive enhancements,with maximum sustained wind speed errors decreasing by 0.26 m/s per year for 120 h forecasts.The study also identifies several key patterns in forecast performance:typhoon-grade or stronger TCs exhibit smaller track errors than week or weaker systems;intensity forecasts systematically overestimate weaker TCs while underestimating stronger systems;and spatial error distributions show greater track inaccuracies near landmasses and regional intensity biases.These findings highlight both the significant advances in TC forecasting capability achieved through improved modeling and observational systems,and the remaining challenges in predicting TC changes and landfall behavior,providing valuable benchmarks for future forecast system development.展开更多
Inborn errors of metabolism(IEM)are rare disorders,most are liver-based with liver transplantation(LT)emerging as an effective cure in the pediatric population.LT has been shown to offer a cure or deter disease progre...Inborn errors of metabolism(IEM)are rare disorders,most are liver-based with liver transplantation(LT)emerging as an effective cure in the pediatric population.LT has been shown to offer a cure or deter disease progression and provide symptomatic improvement in patients with IEM.Each metabolic disorder is unique,with the missing enzyme or transporter protein causing substrate deficiency or toxic byproduct production.Knowledge about the distribution of deficient enzymes,the percentage of enzymes replaced by LT,and the extent of extrahepatic involvement helps anticipate and manage complications in the perioperative period.Most patients have multisystem involvement and can be on complex dietary regimens.Metabolic decompensation can be triggered due to the stress response to surgery,fasting and other unanticipated complications perioperatively.Thus,a multidisciplinary team’s input including those from metabolic specialists is essential to develop disease and patient-specific strategies for the perioperative management of these patients during LT.In this review,we outline the classification of IEM,indications for LT along with potential benefits,basic metabolic defects and their implications,details of extrahepatic involvement and perioperative management strategies for LT in children with some of the commonly presenting IEM,to assist anesthesiologists handling this cohort of patients.展开更多
The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower b...The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.展开更多
Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparam...Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparametric finite element and related methods, the bounds of interpolatio n error for arbitrary narrow quadrilateral quasi-Wilson element are obtained in case when the condition ρ K/h K≥σ 0】0 is not satisfied, where h K is the diameter of the element K and ρ K is the diameter of an ins cribed circle in K. The interpolation error is O(h2 K) in the L2( K)-norm and O(h K) in the H1(K) -norm provided that the in terpolated function belongs to H2(K).展开更多
The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for ...The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation.展开更多
The high level of safety demand of civil aviation requests local area augmentation system （LAAS） extremely high navigation integrity performance. A new LAAS pseudo-range error overbound method is proposed in this pa...The high level of safety demand of civil aviation requests local area augmentation system （LAAS） extremely high navigation integrity performance. A new LAAS pseudo-range error overbound method is proposed in this paper to improve the integrity of LAAS. Firstly, a more practical pseudo-range error distribution model is established. Then, by calculating the relationship between the statistical uncertainty of the model parameter and the integrity risk, a new method is proposed to calculate the pseudo-range error over-bound model. This method can effectively reduce the inflation factor and the resulting conservativeness of the over-bound model. Comparative experiments show that the method proposed in this paper performs better and satisfies the requirements of real applications.展开更多
Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and unif...Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.展开更多
The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction pr...The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i. e. , a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.展开更多
Due to their complex structure,2-D models are challenging to work with;additionally,simulation,analysis,design,and control get increasingly difficult as the order of the model grows.Moreover,in particular time interva...Due to their complex structure,2-D models are challenging to work with;additionally,simulation,analysis,design,and control get increasingly difficult as the order of the model grows.Moreover,in particular time intervals,Gawronski and Juang’s time-limited model reduction schemes produce an unstable reduced-order model for the 2-D and 1-D models.Researchers revealed some stability preservation solutions to address this key flaw which ensure the stability of 1-D reduced-order systems;nevertheless,these strategies result in large approximation errors.However,to the best of the authors’knowledge,there is no literature available for the stability preserving time-limited-interval Gramian-based model reduction framework for the 2-D discrete-time systems.In this article,2-D models are decomposed into two separate sub-models(i.e.,two cascaded 1-D models)using the condition of minimal rank-decomposition.Model reduction procedures are conducted on these obtained two 1-D sub-models using limited-time Gramian.The suggested methodology works for both 2-D and 1-D models.Moreover,the suggested methodology gives the stability of the reduced model as well as a priori error-bound expressions for the 2-D and 1-D models.Numerical results and comparisons between existing and suggested methodologies are provided to demonstrate the effectiveness of the suggested methodology.展开更多
We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap function...We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.展开更多
Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive an...Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.展开更多
We consider the abstract linear inequality system （A, C, b） and give a sufficient condition for the system （A, C, b） to have an error bound, which extends the previous result.
In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and ...Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.展开更多
In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper ...In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper is to establish that r=0,1,2,3.Also,the nanperiodic cases cannot be constructed empoly-ing the methodology of this paper because that will involve several other end conditions entirely different than(1,10).展开更多
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deri...One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.展开更多
Let X be a uniformly smooth real Banach space. tri T:X→X be a con-tinuous and strongly accretive operator. For a given f∈X,define S: X→X by 1)satisfying: Moreover, suppose that {Sxn} and {Syn} are bounded, then {Xn...Let X be a uniformly smooth real Banach space. tri T:X→X be a con-tinuous and strongly accretive operator. For a given f∈X,define S: X→X by 1)satisfying: Moreover, suppose that {Sxn} and {Syn} are bounded, then {Xn} converges strongly to the unique fixed point of S.展开更多
In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, w...In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.展开更多
In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equatio...In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.展开更多
基金supported in part by the Science and Technology Research and Development Foundation of China Academy of Railway Sciences Corporation Limited(Grant No.2023YJ364)in part by National Key R&D Program of China(Grant No.2022YFC3803700)in part by the project of Beijing Laboratory of Advanced Information Networks.
文摘Time synchronization is a prerequisite for ensuring determinism in time-sensitive networking(TSN).While time synchronization errors cannot be overlooked,pursuing minimal time errors may incur unnecessary costs.Using complex network theory,this study proposes a hierarchy for TSN and introduces the concept of bounded time error.A coupling model between traffic scheduling and time synchronization is established,deriving functional relationships among end-to-end delay,delay jitter,gate window,and time error.These relationships illustrate that time errors can trigger jumps in delay and delay jitter.To evaluate different time errors impact on traffic scheduling performance,an end-to-end transmission experiment scheme is designed,along with the construction of a TSN test platform implementing two representative cases.Case A is a closed TSN domain scenario with pure TSN switches emulating closed factory floor network.Case B depicts remote factory interconnection where TSN domains link via non-TSN domains composed of OpenFlow switches.Results from Case A show that delay and delay jitter on a single node are most significantly affected by time errors,up to one gating cycle.End-to-end delay jitter tends to increase with the number of hops.When the ratio of time error bound to window exceeds 10%,the number of schedulable traffic flows decreases rapidly.Case B reveals that when time error is below 1μs,the number of schedulable traffic flows begins to increase significantly,approaching full schedulability at errors below 0.6μs.
基金supported by the National Key R&D Program of China [grant number 2023YFC3008004]。
文摘This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administration.The analysis reveals systematic improvements in both track and intensity forecasts over the decade,with distinct error characteristics observed across various forecast parameters.Track forecast errors have steadily decreased,particularly for longer lead times,while error magnitudes have increased with longer forecast lead times.Intensity forecasts show similar progressive enhancements,with maximum sustained wind speed errors decreasing by 0.26 m/s per year for 120 h forecasts.The study also identifies several key patterns in forecast performance:typhoon-grade or stronger TCs exhibit smaller track errors than week or weaker systems;intensity forecasts systematically overestimate weaker TCs while underestimating stronger systems;and spatial error distributions show greater track inaccuracies near landmasses and regional intensity biases.These findings highlight both the significant advances in TC forecasting capability achieved through improved modeling and observational systems,and the remaining challenges in predicting TC changes and landfall behavior,providing valuable benchmarks for future forecast system development.
文摘Inborn errors of metabolism(IEM)are rare disorders,most are liver-based with liver transplantation(LT)emerging as an effective cure in the pediatric population.LT has been shown to offer a cure or deter disease progression and provide symptomatic improvement in patients with IEM.Each metabolic disorder is unique,with the missing enzyme or transporter protein causing substrate deficiency or toxic byproduct production.Knowledge about the distribution of deficient enzymes,the percentage of enzymes replaced by LT,and the extent of extrahepatic involvement helps anticipate and manage complications in the perioperative period.Most patients have multisystem involvement and can be on complex dietary regimens.Metabolic decompensation can be triggered due to the stress response to surgery,fasting and other unanticipated complications perioperatively.Thus,a multidisciplinary team’s input including those from metabolic specialists is essential to develop disease and patient-specific strategies for the perioperative management of these patients during LT.In this review,we outline the classification of IEM,indications for LT along with potential benefits,basic metabolic defects and their implications,details of extrahepatic involvement and perioperative management strategies for LT in children with some of the commonly presenting IEM,to assist anesthesiologists handling this cohort of patients.
文摘The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.
文摘Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparametric finite element and related methods, the bounds of interpolatio n error for arbitrary narrow quadrilateral quasi-Wilson element are obtained in case when the condition ρ K/h K≥σ 0】0 is not satisfied, where h K is the diameter of the element K and ρ K is the diameter of an ins cribed circle in K. The interpolation error is O(h2 K) in the L2( K)-norm and O(h K) in the H1(K) -norm provided that the in terpolated function belongs to H2(K).
基金Projcct supported by the Natural Science Foundation of China (Grant No. 10371009 ) of Beijing Educational Committee (No. 2002KJ112).
文摘The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation.
基金the National Natural Science Foundation of China(61179054)the National Basic Research Program of China(2011CB707004)the National Key Technology R&D Program(2011BAH24B02)
文摘The high level of safety demand of civil aviation requests local area augmentation system （LAAS） extremely high navigation integrity performance. A new LAAS pseudo-range error overbound method is proposed in this paper to improve the integrity of LAAS. Firstly, a more practical pseudo-range error distribution model is established. Then, by calculating the relationship between the statistical uncertainty of the model parameter and the integrity risk, a new method is proposed to calculate the pseudo-range error over-bound model. This method can effectively reduce the inflation factor and the resulting conservativeness of the over-bound model. Comparative experiments show that the method proposed in this paper performs better and satisfies the requirements of real applications.
基金Project supported by Scientific Research Common Program of Beijing Municipal Commission of Education of China (No.KM200310015060)
文摘Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.
文摘The inverse heat conduction problem （IHCP） is a severely ill-posed problem in the sense that the solution （ if it exists） does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i. e. , a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.
文摘Due to their complex structure,2-D models are challenging to work with;additionally,simulation,analysis,design,and control get increasingly difficult as the order of the model grows.Moreover,in particular time intervals,Gawronski and Juang’s time-limited model reduction schemes produce an unstable reduced-order model for the 2-D and 1-D models.Researchers revealed some stability preservation solutions to address this key flaw which ensure the stability of 1-D reduced-order systems;nevertheless,these strategies result in large approximation errors.However,to the best of the authors’knowledge,there is no literature available for the stability preserving time-limited-interval Gramian-based model reduction framework for the 2-D discrete-time systems.In this article,2-D models are decomposed into two separate sub-models(i.e.,two cascaded 1-D models)using the condition of minimal rank-decomposition.Model reduction procedures are conducted on these obtained two 1-D sub-models using limited-time Gramian.The suggested methodology works for both 2-D and 1-D models.Moreover,the suggested methodology gives the stability of the reduced model as well as a priori error-bound expressions for the 2-D and 1-D models.Numerical results and comparisons between existing and suggested methodologies are provided to demonstrate the effectiveness of the suggested methodology.
基金supported by the National Natural Science Foundation of China (No. 10671050)the Natural Science Foundation of Heilongjiang Province of China (No. A200607)
文摘We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.
基金Project supported by the Major State Basic Research Development Program of China(Grant No.2012CB215202)the National Natural Science Foundation of China(Grant Nos.61104080 and 61134001)the Fundamental Research Funds for the Central Universities(Grant No.CDJZR13 175501)
文摘Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.
基金Supported by the National Science Foundation of China（10361008） Supported by the Natural Science Foundation of Yunnan Province（2003A0002M）
文摘We consider the abstract linear inequality system （A, C, b） and give a sufficient condition for the system （A, C, b） to have an error bound, which extends the previous result.
文摘In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
基金Supported by the Natural Science Foundation of Zhejiang Province（Y6090361）
文摘Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson＇s quadrature rule involving n-time（1 ≤ n ≤ 4） differentiable mappings and then to the estimations of error bounds for the adaptive Simpson＇s quadrature rule.
文摘In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper is to establish that r=0,1,2,3.Also,the nanperiodic cases cannot be constructed empoly-ing the methodology of this paper because that will involve several other end conditions entirely different than(1,10).
文摘One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.
文摘Let X be a uniformly smooth real Banach space. tri T:X→X be a con-tinuous and strongly accretive operator. For a given f∈X,define S: X→X by 1)satisfying: Moreover, suppose that {Sxn} and {Syn} are bounded, then {Xn} converges strongly to the unique fixed point of S.
基金The Project was supported by National Natural Science Foundation of China
文摘In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.
基金This research was supported by the National Natural Science Foundation of China
文摘In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.
