A note on double Laplace decomposition method for solving singular one dimensional pseudo thermo-elasticity coupled system
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Authors
Hassan Eltayeb
- Mathematics Department, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.
Imed Bachar
- Mathematics Department, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.
Abstract
In this paper, Adomain decomposition method is reintroduced with double
Laplace transform methods to obtain closed form solutions of linear and
nonlinear singular one dimensional pseudo thermo-elasticity coupled system.
The nonlinear terms can be easily handled by the use of Adomian polynomials.
Furthermore, we illustrate our proposed methods by one example.
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ISRP Style
Hassan Eltayeb, Imed Bachar, A note on double Laplace decomposition method for solving singular one dimensional pseudo thermo-elasticity coupled system, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 6, 864--876
AMA Style
Eltayeb Hassan, Bachar Imed, A note on double Laplace decomposition method for solving singular one dimensional pseudo thermo-elasticity coupled system. J. Nonlinear Sci. Appl. (2018); 11(6):864--876
Chicago/Turabian Style
Eltayeb, Hassan, Bachar, Imed. "A note on double Laplace decomposition method for solving singular one dimensional pseudo thermo-elasticity coupled system." Journal of Nonlinear Sciences and Applications, 11, no. 6 (2018): 864--876
Keywords
- Double Laplace transform
- inverse Laplace transform
- pseudo thermo-elasticity equation
- single Laplace transform
- decomposition methods
MSC
References
-
[1]
K. Abbaoui, Y. Cherruault, , Convergence of Adomian’s Method Applied to Differential Equations, Comput. Math. Model., 28 (1994), 103–109.
-
[2]
K. Abbaoui, Y. Cherruault , Convergence of Adomian’s Method Applied to Nonlinear Equations, Math. Comput. Modelling., 20 (1994), 69–73.
-
[3]
K. Abbaoui, Y. Cherruault, V. Seng , Practical Formulae for the Calculus of Multivariable Adomian Polynomials, Math. Comput. Modelling., 22 (1995), 89–93.
-
[4]
F. M. Allan, K. Al-khaled, An approximation of the analytic solution of the shock wave equation, J. Comput. Appl. Math., 192 (2006), 301–309.
-
[5]
A. Atangana , Convergence and stability analysis of a novel iteration method for fractional biological population equation, Neural Comput & Applic., 25 (2014), 1021–1030.
-
[6]
A. Atangana , On the new fractional derivative and application to nonlinear Fisher’s reaction-diffusion equation , Appl. Math. Comput., 273 (2016), 948–956.
-
[7]
A. Atangana, S. C. Oukouomi Noutchie, On Multi-Laplace Transform for Solving Nonlinear Partial Differential Equations with Mixed Derivatives, Math. Probl. Eng., 2014 (2014), 9 pages.
-
[8]
E. Babolian, J. Biazar, On the order of convergence of Adomian method , Appl. Math. Comput., 130 (2002), 383–387.
-
[9]
S. M. El-Sayed, D. Kaya , On the numerical solution of the system of two-dimensional Burgers’ equations by the decomposition method, Appl. Math. Comput., 158 (2004), 101–109.
-
[10]
H. Eltayeb, A. Kılıçman , A Note on Solutions of Wave, Laplace’s and Heat Equations with Convolution Terms by Using Double Laplace Transform , Appl. Math. Lett., 21 (2008), 1324–1329.
-
[11]
I. Hashim, M. S. M. Noorani, M. R. Said Al-Hadidi , Solving the generalized Burgers-Huxley equation using the Adomian decomposition method , Math. Comput. Modelling., 43 (2006), 1404–1411.
-
[12]
J.-H. He, Homotopy perturbation method for solving boundary value problems, Phys. Lett. A, 350 (2006), 87–88.
-
[13]
D. Kaya, I. E. Inan, A convergence analysis of the ADM and an application, Appl. Math. Comput., 161 (2005), 1015– 1025.
-
[14]
D. Kaya, I. E. Inan , A numerical application of the decomposition method for the combined KdV–MKdV equation, Appl. Math. Comput., 168 (2005), 915–926.
-
[15]
A. Kılıçman, H. Eltayeb, A note on defining singular integral as distribution and partial differential equation with convolution term, Math. Comput. Modelling., 49 (2009), 327–336.
-
[16]
A. Kılıçman, H. E. Gadain, On the applications of Laplace and Sumudu transforms, J. Franklin Inst., 347 (2010), 848– 862.
-
[17]
H. Lord, Y. Shulman, A generalized dynamical theory of thermo-elasticity , J. Mech. Phys. Solids., 15 (1967), 299–309.
-
[18]
T. Mavoungou, Y. Cherruault , Convergence of Adomian’s method and applications to nonlinear partial differential equations , Kybernetes, 21 (1992), 13–25.
-
[19]
T. Mavoungou, Y. Cherruault , Numerical study of Fisher’s equation by Adomian’s method, Math. Comput. Modelling., 19 (1994), 89–95.
-
[20]
S. Mesloub, F. Mesloub, On a coupled nonlinear singular thermoelastic system , Nonlinear Anal., 73 (2010), 3195–3208.
-
[21]
S. S. Ray , A numerical solution of the coupled sine-gordon equation using the modified decomposition method , Appl. Math. Comput., 175 (2006), 1046–1054.
-
[22]
N. H. Sweilam , Harmonic wave generation in nonlinear thermoelasticity by variational iteration method and adomian’s method, J. Comput. Appl. Math., 207 (2007), 64–72.
-
[23]
N. H. Sweilam, M. M. Khader, Variational iteration method for one dimensional nonlinear thermoelasticity , Chaos Solitons Fractals, 32 (2007), 145–149.
-
[24]
A.-M. Wazwaz, Partial Differential Equations and Solitary Waves Theory, Springer, Berlin (2009)
