Volume 13, Issue 5
A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation with Time Dependent Dispersion Coefficients and Source Terms

Adv. Appl. Math. Mech., 13 (2021), pp. 1005-1026.

Published online: 2021-06

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• 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.

• Keywords

Two-dimensional advection-diffusion equation, time dependent dispersion coefficients, Crank-Nicolson approach, a two-level factored Crank-Nicolson method, stability and convergence rate.

35K20, 65M06, 65M12

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@Article{AAMM-13-1005, author = {Eric and Ngondiep and and 16655 and and Eric Ngondiep}, title = {A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation with Time Dependent Dispersion Coefficients and Source Terms}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {5}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0206}, url = {http://global-sci.org/intro/article_detail/aamm/19252.html} }
TY - JOUR T1 - A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation with Time Dependent Dispersion Coefficients and Source Terms AU - Ngondiep , Eric JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1005 EP - 1026 PY - 2021 DA - 2021/06 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0206 UR - https://global-sci.org/intro/article_detail/aamm/19252.html KW - Two-dimensional advection-diffusion equation, time dependent dispersion coefficients, Crank-Nicolson approach, a two-level factored Crank-Nicolson method, stability and convergence rate. AB -

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.

Eric Ngondiep. (1970). A Two-Level Factored Crank-Nicolson Method for Two-Dimensional Nonstationary Advection-Diffusion Equation with Time Dependent Dispersion Coefficients and Source Terms. Advances in Applied Mathematics and Mechanics. 13 (5). 1005-1026. doi:10.4208/aamm.OA-2020-0206
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