Abstract:

The article is devoted to the numerical solution of the nonlinear inverse problem of identifying the time-dependent junior coefficient of the differential equation of anomalous diffusion. The overdetermination condition is specified $\forall t\in (0,T]$ as a function value at an interior point of the domain, or as an integral of the solution over a spatial domain or part of it. An implicit difference scheme is constructed using the finite difference method. We close it with a discrete analog of the overdetermination condition, and as a result, we obtain a nonlinear system of algebraic equations. For its numerical implementation at each time layer, a non-iteration method based on decomposition into two systems of linear algebraic equations with a tridiagonal matrix is proposed. The results of the computational experiment on test problems showed a fairly high accuracy of the proposed method.