Accession Number : AD0736766

Title :   The Approximate Solution of Nonlinear Fixed Point Operator Equations in Normed Linear Spaces.

Descriptive Note : Technical rept.,

Corporate Author : TEXAS UNIV AUSTIN ELECTRONICS RESEARCH CENTER

Personal Author(s) : O'Donnell,R. P. ; Aggarwal,J. K.

Report Date : 30 AUG 1971

Pagination or Media Count : 210

Abstract : The report presents a class of new algorithms for the approximate determination of the fixed points of 'operators' in normed linear spaces. The method of averaging functional corrections is itself a generalization of the classical method of successive approximations. Theoretical results concerning the convergence characteristics of the new algorithms are presented. The new methods are shown to be superior to the method of averaging functional corrections for certain types of operators. The primary application is to boundary value problems in integral equation form, and the representation of boundary value problems in this form is discussed. Other potential practical applications are considered. Numerical examples are given which demonstrate that the new algorithms are computational methods of significant practical value. (Author)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), (*BOUNDARY VALUE PROBLEMS, APPROXIMATION(MATHEMATICS)), INTEGRAL EQUATIONS, BANACH SPACE, POWER SERIES, MAPPING(TRANSFORMATIONS), ITERATIONS, INEQUALITIES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE