Title: New hybrid method for direct numerical solution of nonlinear second, third and fourth orders ordinary differential equations

Authors: Olusola Ezekiel Abolarin; Bamikole Gbenga Ogunware

Addresses: Mathematics Department, Federal University Oye-Ekiti, Ekiti State, Nigeria ' Mathematics and Statistics Department, Joseph Ayo Babalola University, Ikeji-Arakeji, Osun State, Nigeria

Abstract: A novel and efficient algorithm for the concurrent numerical solution of second, third and fourth orders of ordinary differential equations is studied in this article. Collocation and interpolation technique was employed in the derivation of the method and power series approximate solution was used as the interpolating polynomial. The fourth derivative of the power series was collocated at the entire grid and off-grid points, while the fifth and sixth derivatives of the polynomial were collocated at the endpoint only. Proper investigation of the basic properties of the method was done. The results showed that the new block method applied on a nonlinear second, third and fourth orders of ordinary differential equations were better in terms of accuracy than the existing methods. The proposed method takes away the burden of developing a separate method for the solution of second, third and fourth order initial value problem of ordinary differential equations.

Keywords: hybrid block method; collocation; higher order ODEs; interpolation; power series.

DOI: 10.1504/IJMOR.2022.127378

International Journal of Mathematics in Operational Research, 2022 Vol.23 No.3, pp.285 - 315

Received: 02 Jun 2021
Accepted: 25 Jul 2021
Published online: 01 Dec 2022 *

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