
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 parameterdependent equations (1) F(u,lambda) = y sub o involving a Fredholm operator F between (infinitedimensional) Banach spaces X = Z x lambda and Y, and a finitedimensional parameter space lambda. Differentialgeometric ideas are used to discuss the connection between augmented equations and certain onedimensional submanifolds produced by numerical pathtracing 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 boundaryvalue 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