A collocation framework for numerical reconstruction of the source function in a two-term fractional diffusion problem

Document Type : Research Article

Authors

Sahar Jalalian ¹

Afshin Babaei ¹

Morteza Gachpazan ²

¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

² Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎‎, ‎Mashhad‎, ‎Iran‎.

10.22067/ijnao.2026.97820.1844

Abstract

‎This study develops a new spectral collocation strategy to reconstruct an unknown source term appearing in a two-term time-fractional diffusion model equipped with nonlocal boundary constraints‎. ‎As obtaining an exact solution to such problems is generally intractable‎, ‎a collocation strategy based on Legendre polynomials and Chebyshev nodes is employed to construct the numerical approximation‎. By projecting the fractional-order operators onto a bivariate polynomial basis, the original inverse problem is transformed into a system of linear algebraic equations. The solvability of the resulting system is investigated via the properties of the associated collocation matrix incorporating the fractional dynamics and nonlocal boundary conditions. Moreover, convergence analysis and rigorous error‏. Numerical trials are presented to demonstrate the reliability‎, ‎precision‎, ‎and computational efficiency of the proposed procedure‎.

Keywords

Fractional diffusion equation

Inverse source problem

Nonlocal boundary conditions

Error analysis

Subjects

• Numerical methods for differential equations and its applications

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