Print ISSN: 1681-6900

Online ISSN: 2412-0758

Keywords : stability


Stability and Convergence of Explicit Difference Method for Solving the 3-Dimensional Two-Sided Fractional Diffusion Equation

Iman Isho Gorial

Engineering and Technology Journal, 2012, Volume 30, Issue 5, Pages 832-848

In this paper, a numerical solution of the 3-dimensional two-sided fractional
diffusion equation has been presented. The algorithm for the numerical solution for
this equation is based on explicit finite difference method. The consistency, conditional
stability, and convergence of the fractional order numerical method are described.
The numerical method has been applied to solve a practical numerical example and
the results have been compared with exact solution. The results were presented in
tables using the MathCAD 12 software package when it is needed. The explicit finite
difference method appeared to be effective and reliable in solving the 3-dimensional
two-sided fractional Diffusion equation

Numerical Methods for Fractional Reaction-Dispersion Equation with Riesz Space Fractional Derivative

I. I. Gorial

Engineering and Technology Journal, 2011, Volume 29, Issue 4, Pages 709-715

In this paper, a numerical solution of fractional reaction-dispersion equation with
Riesz space fractional derivative has been presented. The algorithm for the numerical
solution for this equation is based on two finite difference methods. The consistency,
stability, and convergence of the fractional order numerical method are described.
The numerical methods have been applied to solve a practical numerical example
and comparing results with the exact solution. The results were presented in tables
using the MathCAD 12 software package when it is needed. The two finite difference
methods appeared to be effective and reliable in solving fractional reaction-dispersion
equation with Riesz space fractional derivative.