Unconditional Stability and Fourth-Order Convergence of a Two-Step Time Split Explicit/Implicit Scheme for Two-Dimensional Nonlinear Unsteady Convection-Diffusion-Reaction Equation
Year: 2024
Author: Eric Ngondiep, Ali H. Tedjani
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1381–1409
Abstract
This paper deals with an efficient two-step time split explicit/implicit scheme applied to a two-dimensional nonlinear unsteady convection-diffusion-reaction equation. The computational cost of the new algorithm at each time level is equivalent to solving a pentadiagonal matrix 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 substitution method. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2023-0040
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1381–1409
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: 2D nonlinear unsteady convection-diffusion-reaction equation explicit method implicit scheme two-step time split fourth-order explicit/implicit approach unconditional stability error estimates.