Order Conditions of a Class of Three-step Hybrid Methods for y'' = f(x,y)

  • Y. D. Jikantoro Department of Mathematical Sciences, Ibrahim Badamasi Babangida University, PMB 11, Lapai Nigeria
  • I. Musa Department of Mathematical Sciences, Ibrahim Badamasi Babangida University, PMB 11, Lapai Nigeria
  • A. Y. Badeggi Department of Mathematical Sciences, Ibrahim Badamasi Babangida University, PMB 11, Lapai Nigeria
  • A. I. Ma'ali Department of Mathematical Sciences, Ibrahim Badamasi Babangida University, PMB 11, Lapai Nigeria
  • A. M. Tako Department of Mathematical Sciences, Ibrahim Badamasi Babangida University, PMB 11, Lapai Nigeria
DOI: https://doi.org/10.6084/m9.figshare.20758075
Keywords: Hybrid Method, B-series, Order Conditions, Three-step Method, Convergence

Abstract

A theoretical approach of B-series is used to analyze the convergence and order of convergence of a newly introduced class of three-step hybrid methods for integrating systems of special second order ordinary differential equations (ODEs). A straightforward technique that generates algebraic order conditions, which is easier to handle than the well known Taylor series technique, is presented. The validity of the order conditions is tested by deriving a fourth order method and compared with existing methods in the literature.

Published
2022-06-29
How to Cite
Jikantoro, Y. D., Musa, I., Badeggi, A. Y., Ma’ali, A. I., & Tako, A. M. (2022). Order Conditions of a Class of Three-step Hybrid Methods for y’’ = f(x,y). International Journal of Mathematical Sciences and Optimization: Theory and Applications, 8(1), 9 - 21. https://doi.org/10.6084/m9.figshare.20758075
Issue
Vol 8 No 1 (2022)
Section
Articles

Copyright (c) 2022 Y. D. Jikantoro, I. Musa, A. Y. Badeggi, A. I. Ma'ali, A. M. Tako

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This work is licensed under a Creative Commons Attribution 4.0 International License.

This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.