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 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.

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The authors would like to acknowledge the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum and Minerals via the Project FT151003.

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Correspondence to Khaled M. Furati.

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Furati, K.M., Mustapha, K., Sarumi, I.O. et al. Inverse source in two-parameter anomalous diffusion, numerical algorithms, and simulations over graded time meshes. Comp. Appl. Math. 40, 25 (2021).

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  • Microwave heating
  • Inverse source problem
  • Anomalous diffusion
  • Volterra integral equation
  • Collocation method
  • Graded mesh error analysis

Mathematics Subject Classification

  • 35R11
  • 35R30