Higher order uniformly convergent methods for singular perturbation problems

✍ Scribed by Hans-Görg Roos

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 367 KB
• Volume: 116
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(94)80033-2

✦ Synopsis

Until now, the best way to construct high order uniformly convergent schemes for singular perturbation problems was to apply exponentially fitted compact difference schemes. We propose the following approach: firstly solve an auxiliary problem with piecewise or nearly piecewise constant coefficients, secondly improve the approximation iteratively using the defect correction idea and piecewise polynomial approximations of higher order. An important advantage of our approach lies in the fact that it is possible to start from a classical or weak formulation of a boundary value problem. Therefore, the approach is useful for singular perturbations related to ordinary as well as partial differential equations.