A New Block-Predictor Corrector Algorithm for the Solution of y’’’=f(x, y, y’, y’’)

Adetola O. Adesanya, Mfon O. Udo, Adam M. Alkali

Department of Mathematics and Statistics, Cross River University of Technology, Calabar, Nigeria.
Department of Mathematics, Modibbo Adama University of Technology, Yola, Nigeria.

DOI: 10.4236/ajcm.2012.24047                

Abstract

We consider direct solution to third order ordinary differential equations in this paper. Method of collection and interpolation of the power series approximant of single variable is considered to derive a linear multistep method (LMM) with continuous coefficient. Block method was later adopted to generate the independent solution at selected grid points. The properties of the block viz: order, zero stability and stability region are investigated. Our method was tested on third order ordinary differential equation and found to give better result when compared with existing methods.

Keywords

Collection; Interpolation; Power Series; Approximant; Linear Multistep; Continuous Coefficient; Block Method

Conflicts of Interest

The authors declare no conflicts of interest.

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