Adaptive Mesh Selection Strategies for Solving Boundary Value Problems

Abstract

Various adaptive mesh selection strategies for solving two-point boundary value problems are brought together and a limited comparison is made. The mesh strategies are applied using collocation methods, and a careful error analysis is made for some of them. A number of the observations and conclusions are valid for the other noninitial value type methods (and for more general differential equations). The effects of removing regions where the solution has been accurately computed and then separately solving on those regions for which the solution is still poor are investigated. After presenting several representative examples, some conclusions are drawn.