TY - JOUR
T1 - Unconditional Stability and Fourth-Order Convergence of a Two-Step Time Split Explicit/Implicit Scheme for Two-Dimensional Nonlinear Unsteady Convection-Diffusion-Reaction Equation
AU - Ngondiep , Eric
AU - Tedjani , Ali H.
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1381
EP - 1409
PY - 2024
DA - 2024/10
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2023-0040
UR - https://global-sci.org/intro/article_detail/aamm/23472.html
KW - 2D nonlinear unsteady convection-diffusion-reaction equation, explicit method, implicit scheme, two-step time split fourth-order explicit/implicit approach, unconditional stability, error estimates.
AB - <p style="text-align: justify;">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.</p>