A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation with Time Dependent Dispersion Coefficients and Source Terms
Year: 2021
Author: Eric Ngondiep
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 5 : pp. 1005–1026
Abstract
This paper deals with a two-level factored Crank-Nicolson method in an approximate solution of two-dimensional evolutionary advection-diffusion equation with time dependent dispersion coefficients and sink/source terms subjects to appropriate initial and boundary conditions. The procedure consists of reducing problems in many space variables into a sequence of one-dimensional subproblems and then find the solution of tridiagonal linear systems of equations. This considerably reduces the computational cost of the algorithm. Furthermore, the proposed approach is fast and efficient: unconditionally stable, temporal second order accurate and fourth order convergent in space and it improves a large class of numerical schemes widely studied in the literature for the considered problem. The stability of the new method is deeply analyzed using the $L^{\infty}(t_{0},T_{f};L^{2})$-norm whereas the convergence rate of the scheme is numerically obtained in the $L^{2}$-norm. A broad range of numerical experiments are presented and critically discussed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0206
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 5 : pp. 1005–1026
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Two-dimensional advection-diffusion equation time dependent dispersion coefficients Crank-Nicolson approach a two-level factored Crank-Nicolson method stability and convergence rate.
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