A finite difference scheme for time-space fractional distributed-order diffusion eqations with weakly ‎singular ‎solutions

Fardi, Mojtaba; Amini, Ebrahim; Mohammadi, Soheila

doi:10.22055/jamm.2024.44387.2187

A finite difference scheme for time-space fractional distributed-order diffusion eqations with weakly ‎singular ‎solutions

Document Type : Original Paper

Authors

¹ Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran

² Department of Mathematics, Payme Noor University, P. O. Box 19395-4697 Tehran, IRAN

10.22055/jamm.2024.44387.2187

Abstract

‎In this paper‎, ‎the time-space distributed-order fractional diffusion equations with weakly singular solutions are considered‎. We provide the difference scheme using a nonuniform mesh to solve ‎equations‎‎. ‎The stability and convergence of the difference scheme are discussed‎, ‎We prove that the difference scheme is unconditionally stable‎. ‎We find that the difference scheme is convergent‎. ‎We also show that the temporal convergence order on the nonuniform mesh is higher than on the uniform mesh‎. Finally, some numerical examples are given to verify the theoretical analysis‏.

Keywords