NUMERICAL SOLUTIONS FOR SPACE FRACTIONAL DISPERSION EQUATIONS WITH NONLINEAR SOURCE TERMS

被引：16

作者：

Choi, Hong Won ^{[1
]}

Chung, Sang Kwon ^{[2
]}

Lee, Yoon Ju ^{[1
]}

机构：

[1] Seoul Sci High Sch, Dept Math, Seoul 110530, South Korea

[2] Seoul Natl Univ, Dept Math Educ, Seoul 151748, South Korea

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2010年 / 47卷 / 06期

关键词：

fractional differential equation; Riemann-Liouville fractional derivative; Caputo fractional derivative; finite difference scheme; stability; convergence; error estimate; FINITE-DIFFERENCE APPROXIMATIONS;

D O I：

10.4134/BKMS.2010.47.6.1225

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order O(Delta x + Delta t) is obtained in the discrete L-2 norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

引用

页码：1225 / 1234

页数：10

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