Numerical Identification of a Nonstationary Multiplier in the Right-Hand Side of Anomalous Diffusion Equation

In this article, we consider initial-boundary value problem for anomalous diffusion equation in a finite region. In contrast to the classical diffusion equation with partial time derivative, the Gerasimov–Caputo fractional derivative of order $$\alpha$$ ( $$0<\alpha<1$$ ) is taken. To approximate the fractional derivative, traditional liberalization is used. Approximation on time is performed by using implicit finite-difference scheme, approximation on space variables is made by the centered finite difference formula. Computational algorithm of identification of the time-dependent factor of the right-hand side is constructed based on a special decomposition of the discrete analogue of the problem into two grid elliptic problems. The unknown factor is evaluated for every time iteration from observations of the solution at a interior point. The capabilities of the proposed algorithm are presented on several one-dimensional model problems.