SOLUTION OF ORDINARY DIFFERENTIAL EQUATION: PERTURBATION ITERATION METHOD APPROACH

Authors

  • M.A. Ayodele 1Open and Distance Learning Centre, Olabisi Onabanjo University, Ago Iwoye Author
  • O.S Odetunde Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoye Author
  • O.O. Olubanwo Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoye Author
  • A. O. Olasupo Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoye Author
  • A. S. Ajani Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoye Author
  • I. A. Olabanjo Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoye Author

Keywords:

First Order Differential Equations, Perturbation Iteration Algorithms, Perturbation Methods

Abstract

A Perturbation iteration algorithm for solving differential equations of first order is proposed. The applications of the new method to systems of first order ordinary ifferential equations are highlighted with four perturbation parameters considered. The results obtained using the model were compared to the exact solution of a first order ordinary differential equation problem after five iterations were carried out, a minimal error was obtained in the four perturbation parameters considered. Graphical representations of the results clearly show the relationship between the exact solutions and the approximate solutions at each iteration stage.
Based on the results presented, it is concluded that the lower the perturbation parameter, the greater the efficiency of this model. Nevertheless, as the perturbation parameter increases, more iterations is expected to be carried out to get an accurate result. However, the model is efficient in solving first order differential equation. 

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References

Boyaci, H., & Pakdemirli, M. (January, 2007). Generation Of Root Finding Algorithm Via Perturbation Theories And Some Formulas. Manisa, Turkey: Elsevier.

Dolapci, I. T., Senol, M., & Pakdemirli, M. (2013). New Perturbation Iteration Solution For Fredholm And Voterra Integral Equations. Turkey: Creative Commons Attributions.

Aksoy, Y., & Pakdemirli, M. (April, 2010). New Perturbation-Iterations For Bratu-Type Equations. Manisa, Turkey: Elsevier.

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Published

2021-12-01

How to Cite

SOLUTION OF ORDINARY DIFFERENTIAL EQUATION: PERTURBATION ITERATION METHOD APPROACH. (2021). The Transactions of the Nigerian Association of Mathematical Physics, 17, 41 –50. https://nampjournals.org.ng/index.php/tnamp/article/view/198

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