Comparison of collocation methods for the solution of second order non-linear boundary value problems

Abstract

This article concerns the application of cubic spline collocation tau-method for solving non-linear second order ordinary differential equations. Three collocation methods [Taiwo, O.A., 1986, A computational method for ordinary differential equations and error estimation. MSc dissertation, University of Ilorin, Nigeria (unpublished); Taiwo, O.A., 2002, Exponential fitting for the solution of two point boundary value problem with cubic spline collocation tau-method. International Journal of Computer Mathematics, 79(3), 229–306.] are discussed and applied to some second order non-linear problems. They are standard collocation, perturbed collocation, and exponentially fitted collocation. Numerical examples are given to illustrate the accuracy, efficiency and computational cost.

Keywords:

• Collocation approximation
• Perturbed collocation
• Standard collocation
• Exponentially fitted collocation
• Error
• Error estimate
• Cubic spline
• Non-linear problems
• Tau method

Additional information

Notes on contributors

O. A. Taiwo

Email: [email protected]