Time-discretization schema for an integrodifferential Sobolev type equation with integral conditions

The appropriate discretization in time schema is considered for approximating the solution of a nonlinear integro-differential Sobolev type equation with integral conditions. We construct a discrete numerical solution of the discretized problem. Then, some a priori estimates for the approximations are derived, while the convergence of the method and the well posedness of the problem under study are established.