This paper deals with an efficient two-step time split explicit/implicit scheme applied to a two-dimensional nonlinear unsteady convection-diffusionreaction equation.The computational cost of the new algorithm at each...This paper deals with an efficient two-step time split explicit/implicit scheme applied to a two-dimensional nonlinear unsteady convection-diffusionreaction equation.The computational cost of the new algorithm at each time level is equivalent to solving a pentadiagonalmatrix equation with strictly dominant diagonal elements.Such a bandwidth matrix can be easily inverted using the Gaussian Decomposition and the corresponding linear system should be solved by the back substitutionmethod.The proposed approach is unconditionally stable,temporal second-order accuracy and fourth-order convergence in space.These results suggest that the developed technique is faster and more efficient than a large class of numerical methods studied in the literature for the considered initial-boundary value problem.Numerical experiments are carried out to confirm the theoretical analysis and to demonstrate the performance of the constructed numerical scheme.展开更多
文摘This paper deals with an efficient two-step time split explicit/implicit scheme applied to a two-dimensional nonlinear unsteady convection-diffusionreaction equation.The computational cost of the new algorithm at each time level is equivalent to solving a pentadiagonalmatrix equation with strictly dominant diagonal elements.Such a bandwidth matrix can be easily inverted using the Gaussian Decomposition and the corresponding linear system should be solved by the back substitutionmethod.The proposed approach is unconditionally stable,temporal second-order accuracy and fourth-order convergence in space.These results suggest that the developed technique is faster and more efficient than a large class of numerical methods studied in the literature for the considered initial-boundary value problem.Numerical experiments are carried out to confirm the theoretical analysis and to demonstrate the performance of the constructed numerical scheme.
