Layton, William J. Galerkin methods for two-point boundary value problems for first order systems. (English) Zbl 0532.65056 SIAM J. Numer. Anal. 20, 161-171 (1983). The boundary value problem \[ Ay'(t)+By(t)=f(t),\quad 0\leq t\leq 1 \] Cy(0)\(+Dy(1)=0\), is considered where A and B are \(n\times n\) matrices, possibly functions of t, y(t) and f(t) are vector functions, and C and D are matrices chosen so that the problem is well posed. The author suggests a nonstandard Galerkin method of least squares type which in the nonregular case gives slightly more accurate result then standard Galerkin methods. Reviewer: G.Tabidze Cited in 4 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations Keywords:Galerkin methods; first order systems; rigorous upper and lower estimates; optimal accuracy; least-squares method PDFBibTeX XMLCite \textit{W. J. Layton}, SIAM J. Numer. Anal. 20, 161--171 (1983; Zbl 0532.65056) Full Text: DOI