Basic Sciences Group, Golpayegan College of Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
10.22128/ansne.2026.3235.1192
Abstract
In this paper, a collocation approach based on reproducing kernels is presented for the numerical solution of the 2D time-fractional diffusion equation. Some finite-dimensional positive definite reproducing kernel spaces are constructed using the bases of the Fibonacci polynomials. The spatial discretization in the proposed method is based on the Fibonacci polynomial reproducing kernel method, which is combined with a finite difference scheme for temporal discretization. Handling the boundary conditions in the numerical solution of partial differential equations is a challenging issue in numerical methods. To deal with the boundary conditions in the proposed method, the reproducing kernels are constructed in a way that exactly satisfy the boundary conditions. Some numerical simulations are conducted to prove the efficiency and ability of the Fibonacci kernel approach combined with the time-stepping scheme. The numerical results show the effectiveness and accuracy of the proposed method.
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