Akademik Veri Yönetim Sistemi
COMPUTATIONAL & APPLIED MATHEMATICS, cilt.45, sa.2, 2025 (SCI-Expanded, Scopus)
This study focuses on the determination of a time-dependent source term in a time-fractional diffusion equation with nonlocal boundary conditions, utilizing Hermite polynomials in combination with the Residual Power Series Method (RPSM) and the collocation method. The inverse problem is addressed based on available over determined measurement data. Two different approaches are considered for identifying the source term. In the first approach, Hermite polynomials are directly applied to the inverse problem in conjunction with RPSM and the collocation method. In the second approach, the original problem is decomposed into two sub-problems, and the Hermite-based polynomials are subsequently employed with RPSM and the collocation method to reconstruct the source term. Although both approaches yield results that are in close agreement, the second approach demonstrates improved accuracy. Furthermore, the second approach is newly developed to enhance the understanding of the problem and offers potential for extension using alternative polynomial bases. The main contribution of this study is that, two different methods are implemented to obtain better results for the inverse problem of recovering time dependent source term in time fractional diffusion problem. The effectiveness of the proposed methods is supported by several illustrative examples.