Large time behavior of solutions and finite difference scheme to a nonlinear integro-differential equation

The large-time behavior of solutions and finite difference approximations of the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance are studied. Asymptotic properties of solutions for the initial-boundary value problem with homogeneous Dirichlet boundary conditions is considered. The rates of convergence are given too. The convergence of the semidiscrete and the finite difference schemes are also proved.