A numerical method for third-order non-linear boundary-value problems in engineering

Abstract

A second-order method is developed for the numerical solution of a non-linear, third-order, boundary-value (BV) problem. The method arises from a four-point recurrence relation involving exponential terms, these being replaced by Padé approximants. The convergence of the method is discussed. The method is tested on a sandwich beam problem to demonstrate its usefulness.

Keywords:

• Non-linear third-order BV problems
• Padé approximation
• Sandwich beams
• Recurrence relation
• Convergence

Acknowledgements

The first author is grateful to GIK Institute, Pakistan, for granting him leave of absence in summer 2003 to conduct research at Brunel University, Uxbridge, UK.