BibTex RIS Cite

Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method

Year 2017, Volume: 5 Issue: 1, 1 - 13, 01.05.2017

Abstract

In this paper, we consider mostly the inhomogeneous Fitzhugh-Nagumo-Huxley equation with its initial value. Adomian Decomposition Method (ADM), Modified Decomposition Method (MDM) and Laplace Decomposition Method (LDM) are applied to this equation to obtain the solution that satisfies the given initial condition. It can be easily seen that each method gives the exactly same solution. And then, the inhomogeneous Boussinesq equation and another nonlinear partial differential equation subject to given initial values are solved by using LDM. In applications of the methods, it is demonstrated that we get the solution with a fast convergence by using the advantage of the noise terms. Moreover, we do not need to turn the nonlinear terms into linear ones since Adomian polynomials are used. Therefore, it is deduced that these methods are, indeed, effective and suitable for the nonlinear partial differential equations with the initial values.

References

  • References
  • [1] N. Damil, M. Potier-Ferry, A. Najah, R. Chari, H. Lahmam

Adomian Ayrışma Metodu, Değistirilmis Ayrışma Metodu ve Laplace Ayrışma Metodunu Kullanarak Lineer Olmayan Kısmi Türevli Diferansiyel Denklemleri Çözme

Year 2017, Volume: 5 Issue: 1, 1 - 13, 01.05.2017

Abstract

Bu makalede çoğunlukla başlangıç değeri verilen homojen olmayan Fitzhugh-Nagumo-Huxley denklemi ele aldık. Bu denklemin verilen başlangıç değerini sağlayan çözümünü elde etmek için Adomian ayrışma, değiştirilmiş ayrışma ve laplace ayrışma metotları bu denkleme uygulanmıştır. Kolaylıkla görülebilir ki, her bir metot tamamen aynı sonucu vermektedir. Daha sonra, verilen başlangıç değerlerine tabi tutulan homojen olmayan Boussinesq denklemi ve bir başka lineer olmayan kısmi türevli diferansiyel denklem laplace ayrışma metodu kullanarak çözülmüştür. Metotların uygulamalarında parazit terimlerin avantajını kullanarak çözümüm hızlı bir yakınsama ile elde edildiği gösterildi. Bunun yanında, Adomian polinomları kullanıldığından dolayı lineer olmayan terimleri lineer olanlara dönüştürmeye ihtiyacımız yoktur. Bu nedenle, lineer olmayan kısmi türevli diferansiyel denklemlerinde bu metotların gerçekten etkili ve uygun olduğu sonucuna varıldı

References

  • References
  • [1] N. Damil, M. Potier-Ferry, A. Najah, R. Chari, H. Lahmam
There are 2 citations in total.

Details

Other ID JA64ZM34SH
Journal Section Research Article
Authors

Hami Gündoğdu

Ömer Faruh Gözükızıl This is me

Publication Date May 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Gündoğdu, H., & Gözükızıl, Ö. F. (2017). Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method. MANAS Journal of Engineering, 5(1), 1-13.
AMA Gündoğdu H, Gözükızıl ÖF. Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method. MJEN. May 2017;5(1):1-13.
Chicago Gündoğdu, Hami, and Ömer Faruh Gözükızıl. “Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method”. MANAS Journal of Engineering 5, no. 1 (May 2017): 1-13.
EndNote Gündoğdu H, Gözükızıl ÖF (May 1, 2017) Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method. MANAS Journal of Engineering 5 1 1–13.
IEEE H. Gündoğdu and Ö. F. Gözükızıl, “Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method”, MJEN, vol. 5, no. 1, pp. 1–13, 2017.
ISNAD Gündoğdu, Hami - Gözükızıl, Ömer Faruh. “Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method”. MANAS Journal of Engineering 5/1 (May 2017), 1-13.
JAMA Gündoğdu H, Gözükızıl ÖF. Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method. MJEN. 2017;5:1–13.
MLA Gündoğdu, Hami and Ömer Faruh Gözükızıl. “Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method”. MANAS Journal of Engineering, vol. 5, no. 1, 2017, pp. 1-13.
Vancouver Gündoğdu H, Gözükızıl ÖF. Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method. MJEN. 2017;5(1):1-13.

Manas Journal of Engineering 

16155