On numerical solution of third‐order boundary‐value problems

A fourth-order method is developed for the approximation of the solution of certain two-point boundary-value problems involving third-order linear and non-linear differential equations. The method arises from a four-point recurrence relation involving exponential terms, these being replaced by Pade approximants. The convergence of the method is discussed. The method is tested on two problems to demonstrate the practical usefulness of the approach.