Coupled singular and non singular thermoelastic system and Double Laplace Decomposition method

Year 2016, Volume: 4 Issue: 3, 212 - 222, 30.09.2016

Hassan Eltayeb Gadain

Abstract

In this paper, the double Laplace decomposition
methods are applied to solve the non singular and singular one dimensional
thermo-elasticity coupled system. The technique is described and illustrated
with some examples.

Keywords

Double Laplace transform , inverse Laplace transform , nonlinear system partial differential equation , single Laplace transform

References

• N.H. Sweilam and M.M. Khader, Variational iteration method for one dimensional nonlinear thermoelasticity, Chaos, Solitons and Fractals, 32 (2007) 145-149.
• A. Sadighi and D. D. Ganji, A study on one dimensional nonlinear thermoelasticity by Adomian decomposition method, World Journal of Modelling and Simulation, 4 (2008), 19-25.
• Abdou MA, Soliman AA. Variational iteration method for solving Burger’s and coupled Burger’s equations. J Comput Appl Math 181, ( 2)(2005):245-51.
• S. Jiang. Numerical solution for the cauchy problem in nonlinear 1-d-thermoelasticity. Computing, 44(1990) 147-158.
• M. Slemrod. Global existence, uniqueness and asymptotic stability of classical solutions in one dimensional nonlinear thermoelasticity. Arch. Rational Mech. Anal., 76(1981) 97–133.
• C. A. D. Moura. A linear uncoupling numerical scheme for the nonlinear coupled thermodynamics equations. Berlin-Springer, (1983), 204–211. In: V. Pereyra, A. Reinoze (Editors), Lecture notes in mathematics, 1005.
• 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.
• A. Kiliçman and H. E. Gadain, “On the applications of Laplace and Sumudu transforms,” Journal of the Franklin Institute,347(5)(2010) 848–862.
• Abdon Atangana, Convergence and stability analysis of a novel iteration method for fractional biological population equation, Neural Comput & Applic 25 (2014) 1021–1030.
• Abdon Atangana, On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation, Applied Mathematics and Computation 273 (2016) 948–956.
• S. Abbasbandy, Iterated He’s homotopy perturbation method for quadratic Riccati differential equation, Applied Mathematics and Computation 175 (2006) 581–589.
• D.D. Ganji, A. Sadighi, Application of He’s homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations, International Journal of Nonlinear Sciences and Numerical Simulation 7 (4) (2006) 411–418.
• J.H. He, A simple perturbation approach to Blasius equation, Applied Mathematics and Computation 140 (2–3) (2003) 217–222.