×

Introduction to computational methods for differential equations. (English) Zbl 0843.65057

Ainsworth, M. (ed.) et al., Advances in numerical analysis. Vol. IV. Theory and numerics of ordinary and partial differential equations. Proceedings of the sixth SERC summer school in numerical analysis, Leicester, UK, July 18-29, 1994. Oxford: Clarendon Press. Oxford Science Publications. 77-122 (1995).
Summary: We give an introduction to a unified approach to computational methods for differential equations based on Galerkin methods with piecewise polynomial approximation. We present adaptive methods with reliable and efficient control of computational errors and also discuss estimation and control of data and modeling errors. As model problems we consider two-point boundary value problems, initial value problems for ordinary differential equations, the Poisson equation and the heat equation. We present sample results using the Femlab software.
For the entire collection see [Zbl 0836.00040].

MSC:

65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34B15 Nonlinear boundary value problems for ordinary differential equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K05 Heat equation
PDFBibTeX XMLCite