A collocation method for solving a class of singular nonlinear two-point boundary value problems

[摘要] In this paper, an iterative algorithm for serving singular nonlinear two-point boundary value problems is formulated. This method is basically a collocation method for nonlinear second-order two-point boundary value problems with singularities at either one or both of the boundary points. It is proved that the iterative algorithm converges to a smooth approximate solution of the BVP provided the boundary value problem is well posed and the algorithm is applied appropriately. Error estimates for uniform partitions are also investigated. It has been shown that, for sufficiently smooth solutions, the method produces order h(4) approximations. Numerical examples are provided to show the effectiveness of the algorithm.

[发布日期] 1997-10-07

[关键词] singular boundary value problems;approximation;method of collocation;interpolation;iterative method;subdivision algorithm