A Class of Irrational Linear Multistep Block Method for the Direct Numerical Solution of Third Order Ordinary Differential Equations

Bamikole Gbenga Ogunware¹ and Ezekiel Olaoluwa Omole^1,

¹Department of Mathematics and Statistics, Joseph Ayo Babalola University, Ikeji-Arakeji, Osun State, Nigeria

Cite this paper:
Bamikole Gbenga Ogunware and Ezekiel Olaoluwa Omole. A Class of Irrational Linear Multistep Block Method for the Direct Numerical Solution of Third Order Ordinary Differential Equations. Turkish Journal of Analysis and Number Theory. 2020; 8(2):21-27. doi: 10.12691/tjant-8-2-1

Abstract

This work considers the direct solution of general third order ordinary differential equation by three-step irrational linear multistep method. This method is derived using collocation and interpolation techniques. An irrational three-step method is developed. Taylor series and block methods are used to generate the independent solution at selected points. The properties of the method were also determined. The developed method was applied on general third order ordinary differential equations. And the performance of the numerical results of the method compared favourably with the results of existing authors in the recent literature to test its accuracy and stability.

Keywords:
Irrational Linear Multistep Method interpolation collocation third order block and Taylor series

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