A 5-step maximal order method for direct solution of second order Ordinary Differential Equations
In this work, we propose a direct solution of second order ordinary differential equations without reduction to systems of first order equations. The method is based on collocating the differential system arising from a polynomial basis function at selected grid points xn+i, i = 0(1)5, which yields a five-step continuous method. The computational burden and computer time wastage involved in the usual reduction of second order problems into system of first order equations are avoided by this approach. The method is symmetric, consistent and of order nine. The interval of absolute stability of the method is sufficient for moderately stiff problems. The accuracy of the method is shown with some test examples.
Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp. 279-284