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

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.