Numerical solution of a non-local fractional convection-diffusion equation

被引:0
作者
Osorio, F. C. [1 ]
Amador, P. A. [1 ]
Bedoya, C. A. [2 ]
机构
[1] Univ Catolica Pereira, Pereira, Colombia
[2] GESCE, Cali, Colombia
来源
ENTRE CIENCIA E INGENIERIA | 2024年 / 18卷 / 35期
关键词
Finite Differences; Discrete Mollification; Fractional Derivation; Nonlocal Equation; PARTIAL-DIFFERENTIAL-EQUATIONS; FINITE-DIFFERENCE; STABILITY ANALYSIS; APPROXIMATION; SCHEME;
D O I
10.31908/19098367.2954
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This article investigates the numerical solutions of a fractional non -local convection-diffusion equation in time, defined in the Caputo sense. The approximations are developed using an explicit numerical scheme through the finite difference method. Through this discretization and the Von Neumann method, the Courant-Friedrichs-Lewy (CFL) stability condition is established, which demonstrates the monotonicity property and the total variation diminishing (TVD) property, along with some important inequalities for the regularity of the scheme. Finally, some numerical experiments with a source term are presented to find analytical solutions and perform the respective error calculations and convergence orders with the numerical approximation.
引用
收藏
页码:25 / 31
页数:7
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