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V. D. Beibalaev

,

R. P. Meilanov

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.
KEYWORDS
fractional Caputo derivative, approximation, differential equations, numerical methods, stability
PAPER SUBMITTED: 2011-04-21
PAPER REVISED: 2011-07-14
PAPER ACCEPTED: 2011-07-18
DOI REFERENCE: https://doi.org/10.2298/TSCI110421076B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE Issue 2, PAGES [385 - 394]
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The Dirihlet problem for the fractional Poisson’s equation with Caputo derivatives: A finite difference approximation and a numerical solution

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence