A Finite-Difference Scheme for a Linear Multi-Term Fractional-in-Time Differential Equation with Concentrated Capacities

Abstract

In this paper, we consider a linear multi-term subdiffusion equation with coefficients which contain Dirac distributions. Also, we consider subdiffusion equations with dynamical boundary conditions. The existence of generalized solutions of these initial-boundary value problems is proved. An implicit finite difference scheme is proposed and its stability and convergence rate are investigated in both cases. The corresponding difference schemes are tested on numerical examples.