An explicit spectral Tau method with Delannoy polynomials for the time-fractional diffusion equation
Year: 2025
Type: article
Abstract: This paper proposes an explicit numerical scheme based on Delannoy polynomials in conjunction with the tau method for solving the time-fractional diffusion equation involving the Caputo derivative. The proposed method constructs approximate solutions using shifted Delannoy polynomials as basis functions, allowing efficient and accurate treatment of the nonlocal nature of fractional derivatives. The method transforms the time-fractional diffusion problem into a system of algebraic equations, which can be solved explicitly. Several benchmark examples are provided to confirm the efficiency, accuracy, and applicability of the new scheme.
Institutions: Fayoum University, Ain Shams University, Cairo University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414398943