Studies in approximation methods—III: Boundary value ordinary differential equations

Abstract

A numerical comparison is made between the orthogonal collocation and Runge-Kutta techniques for solving boundary value ordinary differential equations. Using various forms of the catalyst effectiveness factor system, it is shown that orthogonal collocation is the computationally superior method; this result also holds for a specific class of initial value problems. A multiple element approach in which the elements are located in an optimal manner is also developed. This optimal procedure holds promise for efficiently solving complicated boundary value problems.