×

On the \(H^{-1}\)-Galerkin method for second-order linear two-point boundary value problems. (English) Zbl 0546.65056

The authors consider \(H^{-1}\)-Galerkin methods for two-point boundary value problems. These \(H^{-1}\) methods were introduced by H. H. Rachford jun. and M. F. Wheeler [Math. Aspects finite Elem. partial Differ. Equat., Proc. Symp. Madison 1974, 353-382 (1974; Zbl 0347.65037)] for the case of Dirichlet boundary conditions. In the present paper the \(H^{-1}\)-methods are formulated subject to further types of boundary conditions, and the corresponding error analysis is performed. The authors refer to a new subroutine package named ROWCOL for the solution of the corresponding linear algebraic systems. The results are illustrated by means of some numerical examples.
Reviewer: E.Wagenführer

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
35K20 Initial-boundary value problems for second-order parabolic equations

Citations:

Zbl 0347.65037
PDFBibTeX XMLCite
Full Text: DOI