Inverse source in two-parameter anomalous diffusion, numerical algorithms and simulations over graded time-meshes

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 r...

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Bibliographic Details
Published in:arXiv.org 2019-12
Main Authors: Furati, Khaled M, Kassem Mustapha, Sarumi, Ibrahim O, Iyiola, Olaniyi S
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Convergence
Finite element method
Mathematical models
Numerical analysis
Parameters
Photoelectric cells
Photoelectricity
Time dependence
Volterra integral equations
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Summary: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 \(t=0\), a graded mesh is used to improve the convergence rate. Numerical experiments are provided to illustrate the expected analytical order of convergence.
ISSN:2331-8422