Accession Number : ADA188648

Title :   Error Questions in the Computation of Solution Manifolds of Parametrized Equations.

Descriptive Note : Technical rept.,

Corporate Author : PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS

Personal Author(s) : Rheinboldt, Werner C

PDF Url : ADA188648

Report Date : Sep 1987

Pagination or Media Count : 20

Abstract : Equilibrium problems for many physical systems are modelled by parameter dependent nonlinear equations F(z,lambda) =0. Under fairly general conditions the set of solutions (z, lambda) of this equation forms a differentiable manifold, and, typically in applications, interest centers not so much on computing a few solutions but rather on analysing the form and special features of this manifold. This paper identifies some of the sources of the errors which are necessarily arising in such a computational analysis. Let X and Y be real Hilbert spaces and F:X approaches the limit of Y a Fredholm mapping of class C sub r, r or = 2, and index p or = 1 for which the domain contains an open set S of X. A point s epsilon X is regular if the Jacobian DF(x) maps X onto Y. Then it is well known that the set of all regular solutions, M = (x ; x epsilon S, F(x) = 0, x regular), is a p-dimensional C sub r-manifold in X without boundary. By restricting consideration to this regular solution manifold it has been assumed that a suitable unfolding of the problem has been chosen.

Descriptors :   *MAPPING(TRANSFORMATIONS), COMPUTATIONS, EQUATIONS, EQUILIBRIUM(GENERAL), ERRORS, HILBERT SPACE, PHYSICAL PROPERTIES, SOLUTIONS(GENERAL), SOURCES, COMBINATORIAL ANALYSIS, FINITE ELEMENT ANALYSIS, BOUNDARY VALUE PROBLEMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE