Unconditional Stability and Fourth-Order Convergence of a Two-Step Time Split Explicit/Implicit Scheme for Two-Dimensional Nonlinear Unsteady Convection-Diffusion-Reaction Equation (Advances in Applied Mathematics and Mechanics, 2024)
This paper deals with an efficient two-step time split explicit/implicitscheme applied to a two-dimensional nonlinear unsteady convection-diffusion-reaction equation. The computational cost of the new algorithm at each time level isequivalent to solving a pentadiagonal matrix equation with strictly dominant diagonalelements. Such a bandwidth matrix can be easily inverted using the Gaussian Decomposition and the corresponding linear system should be solved by the back substitution method. The proposed approach is unconditionally stable, temporal second-orderaccuracy and fourth-order convergence in space. These results suggest that the developed technique is faster and more efficient than a large class of numerical methodsstudied in the literature for the considered initial-boundary value problem. Numericalexperiments are carried out to confirm the theoretical analysis and to demonstrate theperformance of the constructed numerical scheme.