An Order Four Continuous Numerical Method for Solving General Second Order Ordinary Differential Equations

Authors

  • Friday Obarhua
    Department of Mathematical Sciences, The Federal University of Technology, Akure, Nigeria
  • Oluwasemire John Adegboro
    Department of Mathematical Sciences, The Federal University of Technology, Akure, Nigeria

Keywords:

Numerical Scheme, Continuous hybrid method, Zero stability, Linear and nonlinear

Abstract

Continuous hybrid methods are now recognized as efficient numerical methods for problems whose solutions have finite domains or cannot be solved analytically. In this work, the continuous hybrid numerical method for the solution of general second order initial value problems of ordinary differential equations is considered. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is zero stable, consistent, convergent. It is suitable for both non-stiff and mildly-stiff problems and results were found to compete favorably with the existing methods in terms of accuracy.

Dimensions

R. P. K. Chan, P. Leone, & A. Tsai, “Order Conditions and Symmetry for Two-Step Hybrid Methods”, Int. J. Comp. Math. 81 (2004) 1519.

S. Gholamtabar & N. Parandin, “Numerical Solutions of Second-Order Differential Equations by Adam Bashforth Method”, American J. of Engi. Research 3 (2014) 318.

J.D. Lambert & A. Watsan, “A Symmetric Multistep Method for Periodic Initial Value Problem”, Journal of the Institute of Mathematics and its Applications 18 (1976) 189.

M. F. Saravi & S.R. Mirrajei, “Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method”, World Acad. Sci. Eng. Technol. 49 (2009) 1051.

S. J. Kayode and D.O. Awoyemi, “A Multiple Derivative Collocation Method for Fifth Order Ordinary Differential Equations”, J. Math. stat. 6 (2010) 60.

A. Golbabai & M. M. Arabshahi, “Smart Numerov Generalized Alternating Group Explicit (SNAGE-PR (2)) Scheme for 2-Point P.V. Problem”, World Appl. Sci. J. 8 (2010) 267.

S.J. Kayode & A. Adeyeye, “ A 3-Step Hybrid Method for Direct Solution of Second Order Initial Value Problems”, Aust. J. of Basic and Applied Sciences 5 (2011) 2121.

S. J. Kayode & A. Adeyeye, “Two-Step Two-Point Hybrid Methods for General Second Order Differential Equations” Afri. J. of Math. & Compt. Sci. Res. 6 (2013) 191.

S. J. Kayode & F. O. Obarhua, “Continuous y − f unction Hybrid Methods for Direct Solution of Differential Equations”, Intern. J. of Diff. Eq. 12 (2013) 37.

S. J. Kayode & F. O. Obarhua, “3-Step y-function Hybrid Methods for Direct Numerical Integration of Second Order IVPs in ODEs”, Theo. Math. & Appl. 5 (2015) 39.

F.O. Obarhua, “An Efficient Two-Step Symmetric Hybrid Block Method for Solving Second Order Initial Value Problems of Ordinary Differential Equations”, Int. J. of Res. and Sci. Innovation 6 (2019) 200.

A. Konguetsof & T.E. Simos, “An Exponentially Fitted and Trigonometrically Fitted Method for the Numerical Solution of Periodic Initial-Value Problems”, Computers and Mathematics with Appl. 45 (2003) 547.

O. O. Olanegan, D. O. Awoyemi, B.G. Ogunware & F.O. Obarhua, “Continuous double-hybrid point method for the solution of second order ordinary differential equations”, Int. J. of Adv. Sci. & Tech. Res. 5 (2015) 549.

A.O. Adesanya, M.R. Odekunle & A.A. James, “Order Seven Hybrid Methods for the Solution of First Order Ordinary Differential Equations”, Canada Journal on Science and Engineering Mathematics 3 (2012) 154.

T.A. Anake, Continuous Implicit Hybrid One-Step Methods for Solutions of Initial Value Problems of General Second Order Ordinary Differential Equations, Ph.D Thesis, Covenant University, Ota, Nigeria, 2011.

Y.S. Awari, “Derivation and Application of Six-Point Linear Multistep Numerical Method for Solution of Second Order Initial Value Problems”, IOSR Journal of Mathematics 7 (2013) 23.

Published

2021-02-25

How to Cite

An Order Four Continuous Numerical Method for Solving General Second Order Ordinary Differential Equations. (2021). Journal of the Nigerian Society of Physical Sciences, 3(1), 42-47. https://doi.org/10.46481/jnsps.2021.150

Issue

Volume 3, Issue 1, February 2021

Section

Original Research
Copyright & Licensing

How to Cite

An Order Four Continuous Numerical Method for Solving General Second Order Ordinary Differential Equations. (2021). Journal of the Nigerian Society of Physical Sciences, 3(1), 42-47. https://doi.org/10.46481/jnsps.2021.150

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