Inverse source in two-parameter anomalous diffusion, numerical algorithms and simulations over graded time-meshes
Numerical Analysis
2019-12-16 v1 Numerical Analysis
Abstract
We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave heating and light propagation in photoelectric cells. A bi-orthogonal pair of bases is employed to construct a series representation of the solution and a Volterra integral equation for the source term. We develop a numerical algorithm for approximating the unknown time-dependent source term. Due to the singularity of the solution near , a graded mesh is used to improve the convergence rate. Numerical experiments are provided to illustrate the expected analytical order of convergence.
Cite
@article{arxiv.1912.06614,
title = {Inverse source in two-parameter anomalous diffusion, numerical algorithms and simulations over graded time-meshes},
author = {Khaled M. Furati and Kassem Mustapha and Ibrahim O. Sarumi and Olaniyi S. Iyiola},
journal= {arXiv preprint arXiv:1912.06614},
year = {2019}
}