Four-Step Block Method for Solving Third Order Ordinary Differential Equation

K. O. Lawal; Y. A. Yahaya; S. D. Yakubu

doi:https://doi.org/10.14445/22315373/IJMTT-V57P546

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 5 | Year 2018 | Article Id. IJMTT-V57P546 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P546

Four-Step Block Method for Solving Third Order Ordinary Differential Equation

K. O. Lawal , Y. A. Yahaya , S. D. Yakubu

Citation :

K. O. Lawal , Y. A. Yahaya , S. D. Yakubu, "Four-Step Block Method for Solving Third Order Ordinary Differential Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 5, pp. 331-344, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P546

Abstract

In This paper we proposed a Four-Step Block- method of Hybrid Linear Multistep Method derived by collocation and interpolation technique with power series as basis function for direct solution of special third order initial value problem of ordinary differential equation. The basic properties of the block, which include consistency, Zero Stable, order, error constant and region of absolute stability were analysed. From the analysis the block derived was found to be Consistent, Zero stable, convergent and A-stable. Also, the block- method was tested on some numerical examples and the result computed shows the derived block method is more accurate than some existing methods considered in this paper.

Keywords

Zero Stable, Error constant, Region of Absolute stability and Convergence.

References

[1] Adee, S.O., Onumanyi, P., Sirisena, U.W. and Yahaya, Y. A. (2005). Note on starting the Numerov Method more accurately by hybrid formular of order four for initial-value problem. Journal of Computational and Applied Mathematics, vol. 175, pp.369-373. Available: http://www.researchgate.net/publication/236247836
[2] Anake , T.A.(2011). Continuous Implicit Hybrid One-Step Methods for the solution of initial value problems of general second order ordinary differential equations. Ph.d thesis submitted to school of postgraduate studies, Covenant University ,Ota. Available: http://thesis.convenantuniversity.edu.ng/bitstream/handle/123456789/198/CUGpo60192-anake
[3] Awoyemi, D. O. (2003). A P-stable Linear Multistep method for solving general third order ordinary differential equations. International Journal of Computer mathematics ,vol. 80, pp. 987- 993, Available: 10.1080/0020716031000079572
[4] Awoyemi, D. O., Kayode, S. J. and Adoghe, L. O. (2014). A Five Step P-stable method for the numerical integration of third order ordinary differential equations. American Journal of Computational mathematics, 2014, pp.119-126. Available: 10.4236/ajcm2014.4301
[5] Badmus, A. M. and Yahaya, Y.A.(2014). A new Algorithm of obtaining order and error constants of third order Linear Multistep Method (LMM). Astan Journal of Fuzzy and Applied Mathematics, vol. 2, pp. 190-194.Available: http://www.adjournline.com/index. journal=AJFAM& page=article&op=view&path[]=1855
[6] Chollom, J.P., Ndam, J.N. and Kumleng, G. M., (2007). On some properties of Block Linear Multistep Method. Science world Journal, vol. 2, pp. 11-17. Available: http://www.scienceworldjournal.org/article/view/2262
[7] Lambert, J.D. (1973). Computation methods in ordinary differential equations. New York John wiley and sons, 224.
[8] Olabode, B.T. and Yusuph, Y. (2009). A new Block method for special third order ordinary differential equations. Journal of mathematics and Statistics, vol. 5, pp. 167-170. Available:http://docsdrive.com/pdfs/science publication/jmssp/2009/167-170.pdf
[9] Olabode, B. T.and Omole, E. O. (2015). Implicit Hybrid Block Numerov- type method for the direct solution of fourth-order ordinary differential equations. American Journal of Computational and Applied Mathematics, vol. 5, pp. 129-139, Available: 10.5923/j.ajcam 20150505 01
[10] Yusuph Y. and Onumanyi P. (2015).New Multiple FDM through collocation for. y = f (x, y) . Preeceeding of Conference organize by National Mathematical Center Abuja. Abacus, vol. 29, no. 2, pp. 92-100.
[11] Obarhua, F. O., & Kayode , S. J. (2016). Symmetric hybrid Linear Multistep method for General third order differential equations. Open Access Library Journal, 3, 1-8, Available: doi:10.4236/oalib.1102583