An Efficient Zero‐Stable Numerical Method for Fourth‐Order Differential Equations

Abstract

The purpose of this paper is to produce an efficient zero‐stable numerical method with the same order of accuracy as that of the main starting values (predictors) for direct solution of fourth‐order differential equations without reducing it to a system of first‐order equations. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is consistent, symmetric, and of optimal order p = 6. The main predictor for the method is also consistent, symmetric, zero‐stable, and of optimal order p = 6.