Improved implementations of adaptive algorithms in collocation for boundary value problems

Abstract

This paper describes an improved adaptive algorithm for collocation solution of boundary value problems. The mesh selection criterion function of the algorithm is based on the collocation matrix of the solution. Then the implementation is improved using certain local behaviour of the error. The algorithm is examined in a selection of badly behaved problems and it is shown to be highly reliable and promissing.

Keywords:

• Adaptive algorithm
• collocation
• boundary value problem
• criterion function

C.R. Categories:

• G 1.7