Abstract
This article is dedicated to numerically solving the spatially loaded time-fractional diffusion equation with initial and Dirichlet-type boundary conditions. We apply finite difference approximation to the considered problem and use the well-known L1 method to approximate the Caputo fractional derivative. The numerical approximation of the problem yields a loaded implicit difference scheme. To obtain the solution, we employ a special parametric representation of solutions of auxiliary linear systems using the superposition property. In conclusion, we showcase several numerical tests, validate the outcomes, and observe the convergence of errors.
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