Direct integrator of block type methods with additional derivative for general third order initial value problems

Abstract

This paper presents the construction of the two-point and three-point block methods with additional derivatives for directly solving y000=f ðt, y, y0y00Þ. The proposed block methods are formulated using Hermite Interpolating Polynomial and approximate the solution of the problem at two or three-point concurrently. The block methods obtain the numerical solutions directly without reducing the equation into the first order system of initial value problems (IVPs). The order and zero-stability of the proposed methods are also investigated. Numerical results are presented and comparisons with other existing block methods are made. The performance shows that the proposed methods are very efficient in solving the general third order IVPs.