An Order Six Zero-Stable Method for Direct Solution of Fourth Order Ordinary Differential Equations

A zero-stable numerical method for direct solution of fourth order differential equations reduces the computational burden and computer time wastage involved in the method of reducing such equations to a system of first order equations. The method adopted is the collocation of the differential system and the interpolation of the approximate solution to the problem using the power series as a basis function. The method is consistent and symmetric with optimal order p = 6. A consistent and symmetric main predictor of order five is also developed for the evaluation of the implicit scheme.