The Convergence Rate for Difference Approximations to General Mixed Initial-Boundary Value Problems

The convergence rate is investigated for the solutions to difference schemes approximating the mixed initial boundary value problem for general systems of differential equations. It is shown that if an energy estimate holds, then the extra boundary conditions can be of one order lower accuracy without destroying the convergence rate expected from the approximation at inner points. If the maximal order of the derivatives occurring in the boundary conditions is low enough, then even lower accuracy can be permitted for the extra boundary conditions.