
Accession Number : AD0686425
Title : ELLIPSOIDAL BOUNDS FOR THE SOLUTIONS OF SYSTEMS OF ORDINARY LINEAR DIFFERENTIAL EQUATIONS.
Descriptive Note : Interim rept.,
Corporate Author : AEROSPACE RESEARCH LABS WRIGHTPATTERSON AFB OHIO
Personal Author(s) : Guderley,Karl G. ; Keller,Charles L.
Report Date : JAN 1969
Pagination or Media Count : 115
Abstract : An approximate solution for a linear system of ordinary differential equations will fail to satisfy this system by some quantity called the residual. The present report derives a method for determining bounds for the error of the approximate solution from bounds on the residual. The residual and the error are characterized as vectors which lie inside and on the surface of ellipsoids. For an nth order system these ellipsoids are given by symmetric positive definite quadratic forms determined by matrices. The matrix for the residual is assumed given. A differential inequality is derived from which the matrix for the error ellipsoid is computed. The narrowness of the error bounds so obtained is studied on a theoretical basis. (Author)
Descriptors : (*DIFFERENTIAL EQUATIONS, APPROXIMATION(MATHEMATICS)), (*NUMERICAL INTEGRATION, NUMERICAL ANALYSIS), (*NUMERICAL ANALYSIS, ERRORS), BOUNDARY VALUE PROBLEMS, MATRICES(MATHEMATICS), INEQUALITIES, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE