In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite differ...In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.展开更多
In this paper,we have proposed a numerical method for Singularly Perturbed Boundary Value Problems(SPBVPs)of convection-diffusion type of third order Ordinary Differential Equations(ODEs)in which the SPBVP is reduced ...In this paper,we have proposed a numerical method for Singularly Perturbed Boundary Value Problems(SPBVPs)of convection-diffusion type of third order Ordinary Differential Equations(ODEs)in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions.The numerical method combines boundary value technique,asymptotic expansion approximation,shooting method and finite difference scheme.In order to get a numerical solution for the derivative of the solution,the domain is divided into two regions namely inner region and outer region.The shooting method is applied to the inner region while standard finite difference scheme(FD)is applied for the outer region.Necessary error estimates are derived for the method.Computational efficiency and accuracy are verified through numerical examples.The method is easy to implement and suitable for parallel computing.展开更多
文摘In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.
文摘In this paper,we have proposed a numerical method for Singularly Perturbed Boundary Value Problems(SPBVPs)of convection-diffusion type of third order Ordinary Differential Equations(ODEs)in which the SPBVP is reduced into a weakly coupled system of two ODEs subject to suitable initial and boundary conditions.The numerical method combines boundary value technique,asymptotic expansion approximation,shooting method and finite difference scheme.In order to get a numerical solution for the derivative of the solution,the domain is divided into two regions namely inner region and outer region.The shooting method is applied to the inner region while standard finite difference scheme(FD)is applied for the outer region.Necessary error estimates are derived for the method.Computational efficiency and accuracy are verified through numerical examples.The method is easy to implement and suitable for parallel computing.
