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

2019/12/13 by Khaled M. Furati, Furati, Khaled M., Kassem Mustapha +5
Engineering · Mathematics · #65L09 #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1912.06614

openalex publication_date 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an inverse source two-parameter sub-diffusion model subject to a\nnonlocal initial condition. The problem models several physical processes,\namong them are the microwave heating and light propagation in photoelectric\ncells. A bi-orthogonal pair of bases is employed to construct a series\nrepresentation of the solution and a Volterra integral equation for the source\nterm. We develop a numerical algorithm for approximating the unknown\ntime-dependent source term. Due to the singularity of the solution near t=0,\na graded mesh is used to improve the convergence rate. Numerical experiments\nare provided to illustrate the expected analytical order of convergence.\n

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