Mesh selection for stiff two-point boundary value problems
Copyright policy )Mesh selection for stiff two-point boundary value problems
The general structure of COLSYS is reviewed, in particular, some theoretical properties of collocation at Gaussian points are stated and it is demonstrated how these properties lead to the derivation of the algorithms for error estimation and mesh selection. The issue of error estimation for both stiff and non-stiff problems is considered, and special mention is made of an approach to stiff problems in which an error estimate is formed by using the solution at collocation points only. Also, it is demonstrated that the mesh selection algorithm of COLSYS is, in a sense, unstable when dealing with a rapidly varying monitor function. Modifications to the algorithm are suggested, and the question of how to estimate the error best with respect to these modifications is considered. The modifications to both the mesh selection and error estimation algorithms are incorporated into the latest version of COLSYS and tested on a set of linear singular perturbation problems within a continuation framework.
- Imperial College London United Kingdom
Numerical solution of boundary value problems involving ordinary differential equations, collocation, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Multiple scale methods for ordinary differential equations, algorithms, mesh selection, error estimation, Mesh generation, refinement, and adaptive methods for ordinary differential equations, Linear boundary value problems for ordinary differential equations, non-stiff problems, singular perturbation, stiff problems, COLSYS
Numerical solution of boundary value problems involving ordinary differential equations, collocation, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Multiple scale methods for ordinary differential equations, algorithms, mesh selection, error estimation, Mesh generation, refinement, and adaptive methods for ordinary differential equations, Linear boundary value problems for ordinary differential equations, non-stiff problems, singular perturbation, stiff problems, COLSYS
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