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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Veröffentlicht in:arXiv.org 2019-12
Hauptverfasser: Furati, Khaled M, Kassem Mustapha, Sarumi, Ibrahim O, Iyiola, Olaniyi S
Format: Artikel
Sprache:eng
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Zusammenfassung: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