Development of a New One-Step Scheme for the Solution of Initial Value Problem (IVP) in Ordinary Differential Equations

Fadugba Sunday Emmanuel; Falodun Bidemi Olumide

doi:doi:10.11648/j.ijtam.20170302.12

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Development of a New One-Step Scheme for the Solution of Initial Value Problem (IVP) in Ordinary Differential Equations

Fadugba Sunday Emmanuel, Falodun Bidemi Olumide

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2)

Received: 27 October 2016 Accepted: 16 January 2017 Published: 9 February 2017

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Abstract

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.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 2)
DOI	10.11648/j.ijtam.20170302.12
Page(s)	58-63
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Interpolating Function, Initial Value Problem, One-Step Method, Ordinary Differential Equation, Taylor Series

References

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[2]	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.
[3]	Boyce, W. E. and DiPrima, R. C. (2001). Elementary differential equation and boundary value problems. John Wiley and Sons.
[4]	Collatz, L. (1960). Numerical treatment of differential equations. Springer Verlag Berlin.
[5]	Erwin, K. (2003). Advanced engineering mathematics. Eighth Edition, Wiley Publisher.
[6]	Fatunla S. O. (1980): “Numerical integrators for stiff and highly oscillatory differential equations”, Mathematics of Computation 34, 373-390.
[7]	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.
[8]	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.
[9]	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.
[10]	Wallace C. S and Gupta G. K. (1973). General Linear multistep methods to solve ordinary differential equations. The Australian Computer Journal, 5, 62-69.
[11]	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.
[12]	http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/numerical-methods.

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Fadugba Sunday Emmanuel, Falodun Bidemi Olumide. (2017). 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, 3(2), 58-63. https://doi.org/10.11648/j.ijtam.20170302.12

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ACS Style

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. Int. J. Theor. Appl. Math. 2017, 3(2), 58-63. doi: 10.11648/j.ijtam.20170302.12

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AMA Style

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. Int J Theor Appl Math. 2017;3(2):58-63. doi: 10.11648/j.ijtam.20170302.12

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@article{10.11648/j.ijtam.20170302.12,
  author = {Fadugba Sunday Emmanuel and Falodun Bidemi Olumide},
  title = {Development of a New One-Step Scheme for the Solution of Initial Value Problem (IVP) in Ordinary Differential Equations},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {58-63},
  doi = {10.11648/j.ijtam.20170302.12},
  url = {https://doi.org/10.11648/j.ijtam.20170302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170302.12},
  abstract = {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.},
 year = {2017}
}

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TY  - JOUR
T1  - Development of a New One-Step Scheme for the Solution of Initial Value Problem (IVP) in Ordinary Differential Equations
AU  - Fadugba Sunday Emmanuel
AU  - Falodun Bidemi Olumide
Y1  - 2017/02/09
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DO  - 10.11648/j.ijtam.20170302.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
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EP  - 63
PB  - Science Publishing Group
SN  - 2575-5080
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AB  - 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.
VL  - 3
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Author Information

Fadugba Sunday Emmanuel

Department of Mathematics, Ekiti State University, Ado Ekiti, Nigeria
Falodun Bidemi Olumide

Department of Mathematics, University of Ilorin, Ilorin, Nigeria

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APA Style

Fadugba Sunday Emmanuel, Falodun Bidemi Olumide. (2017). 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, 3(2), 58-63. https://doi.org/10.11648/j.ijtam.20170302.12

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ACS Style

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. Int. J. Theor. Appl. Math. 2017, 3(2), 58-63. doi: 10.11648/j.ijtam.20170302.12

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AMA Style

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. Int J Theor Appl Math. 2017;3(2):58-63. doi: 10.11648/j.ijtam.20170302.12

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@article{10.11648/j.ijtam.20170302.12,
  author = {Fadugba Sunday Emmanuel and Falodun Bidemi Olumide},
  title = {Development of a New One-Step Scheme for the Solution of Initial Value Problem (IVP) in Ordinary Differential Equations},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {2},
  pages = {58-63},
  doi = {10.11648/j.ijtam.20170302.12},
  url = {https://doi.org/10.11648/j.ijtam.20170302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170302.12},
  abstract = {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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Development of a New One-Step Scheme for the Solution of Initial Value Problem (IVP) in Ordinary Differential Equations
AU  - Fadugba Sunday Emmanuel
AU  - Falodun Bidemi Olumide
Y1  - 2017/02/09
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170302.12
DO  - 10.11648/j.ijtam.20170302.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 58
EP  - 63
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170302.12
AB  - 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.
VL  - 3
IS  - 2
ER  -

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