This paper presents a comparison among Adomian decomposition method (ADM), Wavelet-Galerkin method (WGM), the fully explicit (1,7) finite difference technique (FTCS), the fully implicit (7,1) finite difference method ...This paper presents a comparison among Adomian decomposition method (ADM), Wavelet-Galerkin method (WGM), the fully explicit (1,7) finite difference technique (FTCS), the fully implicit (7,1) finite difference method (BTCS), (7,7) Crank-Nicholson type finite difference formula (C-N), the fully explicit method (1,13) and 9-point finite difference method, for solving parabolic differential equations with arbitrary boundary conditions and based on weak form functionals in finite domains. The problem is solved rapidly, easily and elegantly by ADM. The numerical results on a 2D transient heat conducting problem and 3D diffusion problem are used to validate the proposed ADM as an effective numerical method for solving finite domain parabolic equations. The numerical results showed that our present method is less time consuming and is easier to use than other methods. In addition, we prove the convergence of this method when it is applied to the nonlinear parabolic equation.展开更多
The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial...The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial direction.In addition to that Stefan blowing is considered.The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit.The primitive mass conservation equation,radial,tangential and axial momentum,heat,nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall(disk surface)and free stream boundary conditions.This highly nonlinear,strongly coupled system of unsteady partial differential equations is normalized with the classical von Kármán and other transformations to render the boundary value problem into an ordinary differential system.The emerging 11th order system features an extensive range of dimensionless flow parameters,i.e.,disk stretching rate,Brownian motion,thermophoresis,bioconvection Lewis number,unsteadiness parameter,ordinary Lewis number,Prandtl number,mass convective Biot number,Péclet number and Stefan blowing parameter.Solutions of the system are obtained with developed semi-analytical technique,i.e.,Adomian decomposition method.Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique.展开更多
In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easi...In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.展开更多
In this paper, a numerical solution of nonlinear partial differential equation, Benjamin-Bona-Mahony (BBM) and Cahn-Hilliard equation is presented by using Adomain Decomposition Method (ADM) and Variational Iteration ...In this paper, a numerical solution of nonlinear partial differential equation, Benjamin-Bona-Mahony (BBM) and Cahn-Hilliard equation is presented by using Adomain Decomposition Method (ADM) and Variational Iteration Method (VIM). The results reveal that the two methods are very effective, simple and very close to the exact solution.展开更多
We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy, which is used in the o...We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy, which is used in the original methods, and then several exact solutions of Einstein equations are obtained, including the black hole solution which is surrounded by quintessence. Moreover, the geometry surface gravity defined by Komar mass is also constructed.Secondly, we use both the Komar mass and the ADM mass to modify such method, and the similar results are obtained.Moreover, with some generalize addition to the definition of the ADM mass, our method can be generalized to global monopole spacetime.展开更多
In this paper, the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM) are applied to solve the multi-pantograph delay equations. The sufficient conditions are given to assure the convergenc...In this paper, the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM) are applied to solve the multi-pantograph delay equations. The sufficient conditions are given to assure the convergence of these methods. Several examples are presented to demonstrate the efficiency and reliability of the ADM and the DTM;numerical results are discussed, compared with exact solution. The results of the ADM and the DTM show its better performance than others. These methods give the desired accurate results only in a few terms and in a series form of the solution. The approach is simple and effective. These methods are used to solve many linear and nonlinear problems and reduce the size of computational work.展开更多
The current study examines the important class of Chebyshev’s differential equations via the application of the efficient Adomian Decomposition Method (ADM) and its modifications. We have proved the effectiveness of ...The current study examines the important class of Chebyshev’s differential equations via the application of the efficient Adomian Decomposition Method (ADM) and its modifications. We have proved the effectiveness of the employed methods by acquiring exact analytical solutions for the governing equations in most cases;while minimal noisy error terms have been observed in a particular method modification. Above all, the presented approaches have rightly affirmed the exactitude of the available literature. More to the point, the application of this methodology could be extended to examine various forms of high-order differential equations, as approximate exact solutions are rapidly attained with less computation stress.展开更多
传统图像去噪法基于有用信息和噪声频率特性的差别实现去噪,实际中,有用信息和噪声在频带上往往存在重叠,因此,传统去噪法在抑制噪声的同时,往往损失了细节信息,使图像变模糊.本文引入稀疏与低秩矩阵分解模型描述图像去噪问题,基于该模...传统图像去噪法基于有用信息和噪声频率特性的差别实现去噪,实际中,有用信息和噪声在频带上往往存在重叠,因此,传统去噪法在抑制噪声的同时,往往损失了细节信息,使图像变模糊.本文引入稀疏与低秩矩阵分解模型描述图像去噪问题,基于该模型,采用交替方向法(Alternating direction method,ADM)得到复原图像.实验证明该方法比常用的中值滤波法更有效地抑制了椒盐噪声,同时更好地保持了原始图像的细节信息.展开更多
文摘This paper presents a comparison among Adomian decomposition method (ADM), Wavelet-Galerkin method (WGM), the fully explicit (1,7) finite difference technique (FTCS), the fully implicit (7,1) finite difference method (BTCS), (7,7) Crank-Nicholson type finite difference formula (C-N), the fully explicit method (1,13) and 9-point finite difference method, for solving parabolic differential equations with arbitrary boundary conditions and based on weak form functionals in finite domains. The problem is solved rapidly, easily and elegantly by ADM. The numerical results on a 2D transient heat conducting problem and 3D diffusion problem are used to validate the proposed ADM as an effective numerical method for solving finite domain parabolic equations. The numerical results showed that our present method is less time consuming and is easier to use than other methods. In addition, we prove the convergence of this method when it is applied to the nonlinear parabolic equation.
文摘The study reveals analytically on the 3-dimensional viscous time-dependent gyrotactic bioconvection in swirling nanofluid flow past from a rotating disk.It is known that the deformation of the disk is along the radial direction.In addition to that Stefan blowing is considered.The Buongiorno nanofluid model is taken care of assuming the fluid to be dilute and we find Brownian motion and thermophoresis have dominant role on nanoscale unit.The primitive mass conservation equation,radial,tangential and axial momentum,heat,nano-particle concentration and micro-organism density function are developed in a cylindrical polar coordinate system with appropriate wall(disk surface)and free stream boundary conditions.This highly nonlinear,strongly coupled system of unsteady partial differential equations is normalized with the classical von Kármán and other transformations to render the boundary value problem into an ordinary differential system.The emerging 11th order system features an extensive range of dimensionless flow parameters,i.e.,disk stretching rate,Brownian motion,thermophoresis,bioconvection Lewis number,unsteadiness parameter,ordinary Lewis number,Prandtl number,mass convective Biot number,Péclet number and Stefan blowing parameter.Solutions of the system are obtained with developed semi-analytical technique,i.e.,Adomian decomposition method.Validation of the said problem is also conducted with earlier literature computed by Runge-Kutta shooting technique.
文摘In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.
文摘In this paper, a numerical solution of nonlinear partial differential equation, Benjamin-Bona-Mahony (BBM) and Cahn-Hilliard equation is presented by using Adomain Decomposition Method (ADM) and Variational Iteration Method (VIM). The results reveal that the two methods are very effective, simple and very close to the exact solution.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11273009 and 11303006
文摘We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy, which is used in the original methods, and then several exact solutions of Einstein equations are obtained, including the black hole solution which is surrounded by quintessence. Moreover, the geometry surface gravity defined by Komar mass is also constructed.Secondly, we use both the Komar mass and the ADM mass to modify such method, and the similar results are obtained.Moreover, with some generalize addition to the definition of the ADM mass, our method can be generalized to global monopole spacetime.
文摘In this paper, the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM) are applied to solve the multi-pantograph delay equations. The sufficient conditions are given to assure the convergence of these methods. Several examples are presented to demonstrate the efficiency and reliability of the ADM and the DTM;numerical results are discussed, compared with exact solution. The results of the ADM and the DTM show its better performance than others. These methods give the desired accurate results only in a few terms and in a series form of the solution. The approach is simple and effective. These methods are used to solve many linear and nonlinear problems and reduce the size of computational work.
文摘The current study examines the important class of Chebyshev’s differential equations via the application of the efficient Adomian Decomposition Method (ADM) and its modifications. We have proved the effectiveness of the employed methods by acquiring exact analytical solutions for the governing equations in most cases;while minimal noisy error terms have been observed in a particular method modification. Above all, the presented approaches have rightly affirmed the exactitude of the available literature. More to the point, the application of this methodology could be extended to examine various forms of high-order differential equations, as approximate exact solutions are rapidly attained with less computation stress.
文摘传统图像去噪法基于有用信息和噪声频率特性的差别实现去噪,实际中,有用信息和噪声在频带上往往存在重叠,因此,传统去噪法在抑制噪声的同时,往往损失了细节信息,使图像变模糊.本文引入稀疏与低秩矩阵分解模型描述图像去噪问题,基于该模型,采用交替方向法(Alternating direction method,ADM)得到复原图像.实验证明该方法比常用的中值滤波法更有效地抑制了椒盐噪声,同时更好地保持了原始图像的细节信息.
