Accession Number : AD0619757

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

Corporate Author : TECHNISCHE HOCHSCHULE MUNICH (WEST GERMANY)

Personal Author(s) : Stetter,Hans J.

Report Date : 28 MAY 1964

Pagination or Media Count : 15

Abstract : 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.

Descriptors :   (*EQUATIONS, ERRORS), (*SERIES(MATHEMATICS), FUNCTIONAL ANALYSIS), NUMERICAL METHODS AND PROCEDURES, NONLINEAR DIFFERENTIAL EQUATIONS, PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, INTEGRAL EQUATIONS

Distribution Statement : APPROVED FOR PUBLIC RELEASE