Implicit Two-point Block Method with Third and Fourth Derivatives for Solving General Second Order ODEs

Abstract

In this paper we present an implicit two-point block method for solving directly the general second order ordinary differential equations (ODEs). The method incorporates the first and second derivatives of f(x, y, y ), which are the third and fourth derivatives of the solution. The method is derived using Hermite Interpolating Polynomial as the basic function. A performance comparison of the two-point block method is compared in term of accuracy to several existing methods, which have order almost equal or higher than that of the new method. Numerical results interpret the accuracy and efficacy of the new m ethod. Application of the new method is discussed.

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