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A new numerical scheme for solving the two dimensional fractional diffusion equation

Altan Koç Dilara, Gülsu Mustafa

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 2

5--16

In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given.

New Numerical Approach for Solving Abel’s Integral Equations

Anapalı Şenel Ayşe, Öztürk Yalçın, Gülsu Mustafa

Foundations of Computing and Decision Sciences

2021

Vol. 46, No. 3

255--271

In this article, we present an efficient method for solving Abel’s integral equations. This important equation is consisting of an integral equation that is modeling many problems in literature. Our proposed method is based on first taking the truncated Taylor expansions of the solution function and fractional derivatives, then substituting their matrix forms into the equation. The main character behind this technique’s approach is that it reduces such problems to solving a system of algebraic equations, thus greatly simplifying the problem. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. Figures and tables are demonstrated to solutions impress. Also, all numerical examples are solved with the aid of Maple.