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

‎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.

کلیدواژه ها:

Fractional diffusion equation ، Inverse source problem ، Nonlocal boundary conditions ، error analysis