A novel three-level time-split approach for solving two-dimensional nonlinear unsteady convection-diffusion-reaction equation

Volume 26, Issue 3, pp 222--248 http://dx.doi.org/10.22436/jmcs.026.03.03

Publication Date: November 09, 2021 Submission Date: August 12, 2021 Revision Date: September 02, 2021 Accteptance Date: October 07, 2021

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Authors

E. Ngondiep - Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 90950 Riyadh, Saudi Arabia. - Hydrological Research Centre, Institute for Geological and Mining Research, 4110 Yaounde, Cameroon.

Abstract

This paper considers a deep analysis of a three-level explicit time-split MacCormack method, namely the locally one-dimensional explicit MacCormack for the numerical solution of the two-dimensional nonlinear evolutionary advection-diffusion equation subjects to suitable initial and boundary conditions. The splitting reduces the computational cost of the algorithm. Under a suitable time-step restriction, both theoretical and numerical results on the stability and error estimates of the scheme are deeply analyzed in \(L^{m}(0,T;L^{2})\)-norm (\(m=1,2,\infty\)). The numerical experiments suggest that the proposed algorithm is easy to implement, temporal second-order convergent and fourth-order accurate in space. This shows the utility and efficiency of the considered method.

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Keywords

• invex set
• one-dimensional operators (splitting)
• explicit MacCormack scheme
• three-level explicit time-split MacCormack method
• stability and convergence rate

MSC

•  65M10
•  65M05

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