A numerical method for a time-fractional advection-dispersion equation with a nonlinear source term

被引：4

作者：

Mejia, Carlos E. ^{[1
]}

Piedrahita, Alejandro ^{[2
]}

机构：

[1] Univ Nacl Colombia, Escuela Matemat, Medellin, Colombia

[2] Univ Antioquia, Inst Matemat, Medellin, Colombia

来源：

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2019年 / 61卷 / 1-2期

关键词：

Caputo fractional derivative; Two dimensional time fractional advection-dispersion problem; Finite difference approximation; Stability; Convergence; DIFFUSION EQUATION; ORDER;

D O I：

10.1007/s12190-019-01266-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we propose an implicit finite-difference scheme to approximate the solution of an initial-boundary value problem for a time-fractional advection-dispersion equation with variable coefficients and a nonlinear source term. The time fractional derivative is taken in the sense of Caputo. The method is unconditionally stable and convergent. Some numerical examples are included and the results confirm the theoretical analysis. One of the examples is the fractional Fisher equation of mathematical biology.

引用

页码：593 / 609

页数：17

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