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International Journal of Mathematical Research

February 2017, Volume 6, 2, pp 53-59

Lobatto-Runge-Kutta Collocation and Adomian Decomposition Methods on Stiff Differential Equations

E. U. Agom

,

F. O. Ogunfiditimi

,

Edet Valentine Bassey

E. U. Agom 1 ,

F. O. Ogunfiditimi 2
Edet Valentine Bassey 1 
  1. Department of Mathematics University of Calabar Calabar Nigeria 1

  2. Department of Mathematics University of Abuja Abuja Nigeria 2

Pages: 53-59

DOI: 10.18488/journal.24.2017.62.53.59

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Article History:

Received: 20 June, 2017
Revised: 13 November, 2017
Accepted: 28 December, 2017
Published: 18 December, 2017


Abstract:

In this paper, we show the parallel of Adomian Decomposition Method (ADM) and Lobatto-Runge-Kutta Collocation Method (LRKCM) on first order initial value stiff differential equations. The former method provided closed form solutions while the latter gave approximate solutions. We illustrated these findings in two numerical examples. ADM solutions were in series form while those of LRKCM gave sizeable absolute error. We further visualized our findings in respective plots to show the great potentials of ADM over LRKCM in providing analytical solutions to stiff differential equations.

Contribution/ Originality
This study contributes in showing the originality of ADM in obtaining exact solution to Stiff differential equations, while LRKCM provided approximate solution whose accuracy depended on step size.

Keywords:

Stiff differential equations, Adomian decomposition method, Lobatto-Runge-Kutta collocation method.

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Reference:

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[7]         E. U. Agom and F. O. Ogunfiditimi, "Numerical solution of third-order time invariant linear differential equations by adomian decomposition method," International Journal of Engineering and Science, vol. 16, pp. 81-85, 2016. View at Google Scholar 

[8]         E. U. Agom, F. O. Ogunfiditimi, and P. N. Assi, "On Adomian polynomial and its applications to Lane-Emden type of equation," International Journal of Mathematical Research, vol. 6, pp. 13-21, 2017. View at Google Scholar | View at Publisher

[9]         E. U. Agom, F. O. Ogunfiditimi, and P. N. Assi, "Numerical application of  Adomian decomposition method to fifth-order autonomous differential equations," Journal of Mathematical and Computational Science, vol. 3, pp. 554-563, 2017. View at Google Scholar 

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Funding:

The study received no formal support.

Competing Interests:

The authors declares that they are no competing interest.

Acknowledgement:

E. U. Agom conceptualized, designed and carried out the study supervised by F. O. Ogunfiditimi and Edet Valentine Bassey gave information on multistep collocation method. The authors greatly acknowledge the role, thorough and valuable comments by the supervisor (F. O. Ogunfiditimi).

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