Abstract
This paper presents the construction of the two-point and three-point block methods with additional derivatives for directly solving [Formula: see text]. 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.
Highlights
Olabode[1] used block multistep method to solve special third order initial value problems (IVPs) of ordinary differential equations (ODEs)
Bolaji et al.[5] developed a 1-step implicit block method using collocation technique to find the approximations of third order ODEs where three substep methods were considered
We focus on the derivation of twopoint and three-point block methods for solving general third order IVPs, which approximate the solution to the IVP at two or three-point simultaneously
Summary
Olabode[1] used block multistep method to solve special third order initial value problems (IVPs) of ordinary differential equations (ODEs). Majid et al.[2] derived a two-point implicit block direct integration method to solve third order IVPs. This method estimates the solutions of the IVPs at two points concurrently. Most of the methods were derived using interpolation and collocation technique, the points need to be collocated and interpolated after which a system of linear equations need to be solved simultaneously to obtain the coefficient of the block methods.
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