A Numerical Scheme to Solve an Inverse Problem Related to a Time-Fractional Diffusion-Wave Equation with an Unknown Boundary Condition

Abstract

In the present research, a time fractional inverse diffusion-wave problem of finding the inaccessible boundary value, by the input data at an interior point, is investigated. The numerical algorithm is based on the marching finite difference method. Because of ill-posedness of this inverse problem, we apply the mollification regularization technique to obtain a stable numerical solution. It is proven that the numerical scheme is stable and convergent. In the end, the performance of the proposed numerical approach is assessed by some test examples.