Volume 3, Issue 2, April 2017, Page: 58-63
Development of a New One-Step Scheme for the Solution of Initial Value Problem (IVP) in Ordinary Differential Equations
Fadugba Sunday Emmanuel, Department of Mathematics, Ekiti State University, Ado Ekiti, Nigeria
Falodun Bidemi Olumide, Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Received: Oct. 27, 2016;       Accepted: Jan. 16, 2017;       Published: Feb. 9, 2017
DOI: 10.11648/j.ijtam.20170302.12      View  2934      Downloads  119
In this paper, a new one-step scheme was developed for the solution of initial value problems of first order in ordinary differential equations. In its development a combination of interpolating function and Taylor series were used. The method was used for the solution of initial value problems emanated from real life situations. The numerical results showed that the new scheme is consistent, robust and efficient.
Interpolating Function, Initial Value Problem, One-Step Method, Ordinary Differential Equation, Taylor Series
To cite this article
Fadugba Sunday Emmanuel, Falodun Bidemi Olumide, Development of a New One-Step Scheme for the Solution of Initial Value Problem (IVP) in Ordinary Differential Equations, International Journal of Theoretical and Applied Mathematics. Vol. 3, No. 2, 2017, pp. 58-63. doi: 10.11648/j.ijtam.20170302.12
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Areo E. A. and Adeniyi R. B. (2014). Block implicit one-step method for the numerical integration of initial value problems in ordinary differential equations. International Journal of Mathematics and Statistics studies, 2 (3), 4-13.
Aboiyar T., Luga T. and Ivorter B. V. (2015). Derivation of continuous linear multistep methods using Hermite polynomials as Basis functions. American Journal of Applied Mathematics and Statistics, 3 (6), 220-225.
Boyce, W. E. and DiPrima, R. C. (2001). Elementary differential equation and boundary value problems. John Wiley and Sons.
Collatz, L. (1960). Numerical treatment of differential equations. Springer Verlag Berlin.
Erwin, K. (2003). Advanced engineering mathematics. Eighth Edition, Wiley Publisher.
Fatunla S. O. (1980): “Numerical integrators for stiff and highly oscillatory differential equations”, Mathematics of Computation 34, 373-390.
Gilat, A. (2004). Matlab: An introduction with application. John Wiley and Sons. Gautschi W. (1961): “Numerical integration of ordinary differential equations based on trigonometric polynomials”, NumerischeMathematik 3, 381-397.
Kayode S. J., Ganiyu A. A., and Ajiboye A. S. (2016). On one-step method of Euler-Maruyana type for solution of stochastic differential equations using varying stepsizes. Open Access Library Journal.
Ogunrinde R. B. and Fadugba S. E. (2012). Development of a new scheme for the solution of initial value problems in ordinary differential equations. IOSR Journal of Mathematics, 2, 24-29.
Wallace C. S and Gupta G. K. (1973). General Linear multistep methods to solve ordinary differential equations. The Australian Computer Journal, 5, 62-69.
Ying T. Y., Zurni O. and Kamarun H. M. (2014). Modified exponential rational methods for the numerical solution of first order initial value problems. Sains Malaysiana, 43(12), 1951-1959.
Browse journals by subject