Accession Number : ADA130186

Title :   Solution Manifolds and Submanifolds of Parametrized Equations and Their Discretization Errors.

Descriptive Note : Technical rept.,

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

Personal Author(s) : Fink,James P ; Rheinboldt,Werner C

PDF Url : ADA130186

Report Date : Jan 1983

Pagination or Media Count : 44

Abstract : The paper concerns solution manifolds of nonlinear parameter-dependent equations (1) F(u,lambda) = y sub o involving a Fredholm operator F between (infinite-dimensional) Banach spaces X = Z x lambda and Y, and a finite-dimensional parameter space lambda. Differential-geometric ideas are used to discuss the connection between augmented equations and certain one-dimensional submanifolds produced by numerical path-tracing procedures. Then, for arbitrary (finite) dimension of lambda, estimates of the error between the solution manifold of (1) and its discretizations are developed. These estimates are shown to be applicable to rather general nonlinear boundary-value problems for partial differential equations. (Author)

Descriptors :   *Nonlinear differential equations, *Operators(Mathematics), *Banach space, Errors, Estimates, Parametric analysis, Boundary value problems, Partial differential equations, Approximation(Mathematics)

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE