L1 type approximation of a temporally loaded time-fractional diffusion equation

In this research paper, we study the loaded type time-fractional diffusion equation with temporal loads. We construct a numerical scheme by the finite difference approximation of the considered problem using the well-known L1 scheme to approximate the involved Caputo derivative and central difference scheme for the diffusion term. The linear loaded term in the scheme is dealt with the superposition property of systems of linear algebraic equations by employing a special parametric representation of their solutions with specific structures depending on the difference approximation of the problem. Some numerical results are provided for validating the proposed scheme and studying the errors.