On the Relative Efficiency of Higher Order Collocation Methods for Solving Two-Point Boundary Value Problems

Numerical results are presented which indicate that collocation methods using C¹ piecewise polynomial functions with Gauss collocation points are more efficient than conventional second order finite difference methods for certain nonlinear two-point boundary value problems. For the problems studied, one obtains more accuracy per dollar of computer time with higher order collocation methods. Also for a given accuracy, higher order collocation methods require less computer storage than low order collocation methods or conventional second order finite difference methods.