THE DIRIHLET PROBLEM FOR THE FRACTIONAL POISSON'S EQUATION WITH CAPUTO DERIVATIVES: a finite difference approximation and a numerical solution
Abstract
A finite difference approximation for the Caputo fractional derivative of the 4 - β, 1 < β ≤ 2 order has been developed. A difference schemes for solving the Dirihlet's problem of the Poisson's equation with fractional derivatives has been applied and solved. Both the stability of difference problem in its right-side part and the convergence have been proved. A numerical example was developed by applying both the Liebman and the Monte-Carlo methods.
Dates
- Submission Date2011-04-21
- Revision Date2011-07-14
- Acceptance Date2011-07-18
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Volume
16,
Issue
2,
Pages385 -394