Finite difference scheme for one nonlinear parabolic integro-differential equation

Initial–boundary value problem with mixed boundary conditions for one nonlinear parabolic integro-differential equation is considered. The model is based on Maxwell system describing the process of the penetration of a electromagnetic field into a substance. Unique solvability and asymptotic behavior of solution are fixed. Main attention is paid to the convergence of the finite difference scheme. More wide cases of nonlinearity that already were studied are investigated.