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

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.