Hybrid-Block Numerical Method for Solving Second Order Ordinary Differential Equations
DOI:
https://doi.org/10.33959/cuijca.v3i2.26Abstract
In this work, a new hybrid-block method for the solution of second order ordinary differential equation is developed using power series as the basis function. The developed scheme was used to solve some problems and the result compare with existing results to ascertain the superiority of the new methodReferences
S.O. Fatunla, Block methods for second order IVPs. International Journal of
Computer Mathematics, 42(9), (1991), 55-63.
S.O. Fatunla, Block methods for second order initial value problems. International Journal of Computer Mathematics, 41, (1994), 55-63.
D.O. Awoyemi, A class of continuous Stormer-Cowell type methods for special
second order ordinary differential equations. Spectrum Journal, 5(1 & 2), (1998),100-108.
Z.B. Omar, & M.B. Suleiman, solving second order ODEs directly using parallel 2-point explicit block method. Prosiding Kolokium Kebangsaan Pengintegrasian Teknologi Dalam Sains Matematik, Universiti Sains Malaysia, (1999), 390-395
P. Onumanyi, U.W. Sinsena, & Y. Dauda, Toward uniformly accurate continuous finite difference approximation of ordinary differential equations. Bagale Journal of Pure and Applied Science, 1(2001), 5-8.
T.E. Simos, Dissipative trigonometrically-fitted methods for second order IVPs with oscillating solutions. Int. J. Mod. Phys, (2002), 13(10), 1333-1345.
Z. Omar, & M. Suleiman, Parallel R-point implicit block method for solving higher order ordinary differential equation directly. Journal of ICT., (2003), 3(1), 53-66.
Y.S. Awari & AA. Abada, A class of seven-point zero stable continuous block method for solution of second order ordinary differential equation. International Journal of Mathematics and Statistics Invention (IJMSI), 2(2014), 47-54
Y. Yusuph, & P. Onumanyi, New Multiple FDMs through Multistep Collocation for y''= f(x; y). In: Proceedings of the Conference Organized by the National Mathematical Center, Abuja, Nigeria. (2005)
S.O. Adee et al, Note on starting the Nemerov method more accurately by a
hybrid formula of order four for an initial??value problem. Journal of Computational and Applied Mathematics, 175(2005) 369??373
Z.B. Omar, & M.B. Suleiman, Solving Higher Order ODEs Directly Using Parallel 2-point Explicit Block Method. Matematika, (2005), 21(1), 15-23.
Z.A. Majid, M.B. Suleiman & Z. Omar, 3-point implicit block method for solving ordinary differential equations. Bulletin of the Malaysian Mathematical Sciences Society (2006), (2), 29(1), 23-31.
Z.A. Majid & M.B. Suleiman, Two-point block direct integration implicit variable step method for solving higher order systems of ordinary differential equations. In: Proceedings of the World Congress on Engineering II, (2007), 812-815.
S.N. Jator, A sixth order linear multistep method for the direct solution of
y^''=f(x,y,y^'). International Journal of Pure and Applied Mathematics, (2007), 40(4), 457-472.
A.O. Adesanya, T.A. Anake, & M.O. Udoh, Improved continuous method for
direct solution of general second order ordinary differential equations. Journal of Nigerian Association of Mathematical Physics, 13(2008), 59-62.
A.O. Adesanya, T.A. Anake, & G.J. Oghoyon, Continuous implicit method for the solution of general second order ordinary differential equations. Journal of Nigerian Association of Mathematical Physics, 15(2009), 71-78.
A.M. Badmus, & Y.A. Yahaya, An accurate uniform order 6 block method for direct solution of general second order ordinary differential equations. Pacific Journal of Science and Technology, (2009), 10(2), 248-254.
Z.A. Majid, N.A. Azimi, & M. Suleiman, Solving second order ordinary
differential equations using two-point four step direct implicit block method. European Journal of Scientific Research, (2009), 31(1), 29-36.
Z.B. Ibrahim, M. Suleiman & K.I. Othman, Direct block backward differentiation formulas for solving second order ordinary differential equations. (2009).
S.N. Jator, & J. Li, A self-starting linear multistep method for a direct solution of the general second-order initial value problem. International Journal of Computer Mathematics, (2009), 86(5), 827-836.
T. A. Anake, D. O. Awoyemi and A. A. Adesanya, One-step implicit hybrid block method for the direct solution of general second order ordinary differential equations, IAENG International Journal of Applied Mathematics, 42 (2012), no. 4, 224-228.
T. A. Anake, D. O. Awoyemi and A. A. Adesanya, A one step method for the solution of general second order ordinary differential equations, International Journal of Science and Technology, 2 (2012), no. 4, 159- 163.
D. O. Awoyemi, E. A. Adebile, A. O. Adesanya and T. A. Anake, Modified block method for the direct solution of second order ordinary differential equations, International Journal of Applied Mathematics and Computation, 3 (2011), no. 3, 181-188.
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 Yeak Su Hoe
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
You are free to:
Share - copy and redistribute the material in any medium or format
Adapt - remix, transform, and build upon the material
The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
Attribution - You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
Non Commercial - You may not use the material for commercial purposes.
No additional restrictions - You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
_.jpg)
