A note on double Laplace decomposition method and nonlinear partial differential equations

Yıl 2017, Cilt: 5 Sayı: 4, 156 - 164, 01.10.2017

Hassan Eltayeb

https://izlik.org/JA43JW34BY

Öz

In this
article we propose a new technique, namely double Laplace decomposition method
for solving nonlinear partial differential equation. The technique is described
and illustrated with some examples.

Anahtar Kelimeler

Double Laplace transform , inverse laplace transform

Kaynakça

• A. M. Wazwaz, A new technique for calculating adomian polynomials for nonlinear polynomials. Appl. Math. Comput. 111( 2002) 33 - 51.
• A. Kiliçman and H. E. Gadain, “On the applications of Laplace and Sumudu transforms,” Journal of the Franklin Institute, vol. 347, no. 5, pp. 848–862, 2010.
• H. Eltayeb and A. Kiliçman, A Note on Double Laplace Transform and Telegraphic Equations. Abstract and Applied Analysis, Volume 2013 (2013), Article ID 932578, 6 pages.
• A. Kiliçman and H. Eltayeb, A note on defining singular integral as distribution and partial differential equation with convolution term, Math. Comput. Modelling 49 (2009) 327-336.
• H. Eltayeb and A. Kiliçman, A Note on Solutions of Wave, Laplace’s and Heat Equations with Convolution Terms by Using Double Laplace Transform: Appl, Math, Lett. 21 (12) (2008), 1324–1329.
• D. Kaya and M. Inc. On the Solution of the Nonlinear Wave Equation by the Decomposition Method, Bull. Malaysian Math. Soc. (Second Series) 22 (1999) 151-155.
• A. M. Wazwaz, Partial differential equations methods and applications, Netherland Balkema Publisher, 2002.
• Mohammad Ghoreishi. Adomian Decomposition Method (ADM) for Nonlinear Wave-like Equations with Variable Coefficient, Applied Mathematical Sciences, Vol. 4, 2010, no. 49, 2431 - 2444.