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

• Published in: Computational & applied mathematics Vol. 40; no. 1
• Main Authors: Furati, Khaled M., Mustapha, Kassem, Sarumi, Ibrahim O., Iyiola, Olaniyi S.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2021; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Applied physics; Approximation; Collocation methods; Computational mathematics; Computational Mathematics and Numerical Analysis; Convergence; Finite element method; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematical models; Mathematics; Mathematics and Statistics; Numerical analysis; Parameters; Photoelectric cells; Photoelectricity; Time dependence; Volterra integral equations; Graded mesh error analysis; Inverse source problem; 35R30; Anomalous diffusion; 35R11; Volterra integral equation; Microwave heating; Collocation method
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-020-01399-x

We consider an inverse source two-parameter sub-diffusion model subject to a non-local 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 stable numerical algorithm, based on discontinuous collocation method, for approximating the unknown time-dependent source term. Due to the singularity of the solution near t = 0 , a graded mesh is used to maintain optimal convergence rates, both theoretically and numerically. Numerical experiments are provided to illustrate the expected analytical order of convergence.