ASYMPTOTIC EXPANSIONS FOR THE ERROR OF DISCRETIZATION ALGORITHMS FOR NON-LINEAR FUNCTIONAL EQUATIONS,

The existence of asymptotic expansions of the discretization error is proved for a very general class of discretization algorithms for nonlinear functional equations in Banach spaces. The theorem is applied to initial and boundary value problems for both ordinary and partial differential equations, integral equations, and integrodifferential equations. The first terms of the asymptotic expansion are calculated for a nonlinear boundary value problem of the third kind. It is shown that the actual error of the numerical solution of the problem is well represented.