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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.

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

Hassan Eltayeb Gadain

Abstract

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.
There are 14 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hassan Eltayeb Gadain

Publication Date September 30, 2016
Published in Issue Year 2016 Volume: 4 Issue: 3

Cite

APA Gadain, H. E. (2016). Coupled singular and non singular thermoelastic system and Double Laplace Decomposition method. New Trends in Mathematical Sciences, 4(3), 212-222.
AMA Gadain HE. Coupled singular and non singular thermoelastic system and Double Laplace Decomposition method. New Trends in Mathematical Sciences. September 2016;4(3):212-222.
Chicago Gadain, Hassan Eltayeb. “Coupled Singular and Non Singular Thermoelastic System and Double Laplace Decomposition Method”. New Trends in Mathematical Sciences 4, no. 3 (September 2016): 212-22.
EndNote Gadain HE (September 1, 2016) Coupled singular and non singular thermoelastic system and Double Laplace Decomposition method. New Trends in Mathematical Sciences 4 3 212–222.
IEEE H. E. Gadain, “Coupled singular and non singular thermoelastic system and Double Laplace Decomposition method”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 212–222, 2016.
ISNAD Gadain, Hassan Eltayeb. “Coupled Singular and Non Singular Thermoelastic System and Double Laplace Decomposition Method”. New Trends in Mathematical Sciences 4/3 (September 2016), 212-222.
JAMA Gadain HE. Coupled singular and non singular thermoelastic system and Double Laplace Decomposition method. New Trends in Mathematical Sciences. 2016;4:212–222.
MLA Gadain, Hassan Eltayeb. “Coupled Singular and Non Singular Thermoelastic System and Double Laplace Decomposition Method”. New Trends in Mathematical Sciences, vol. 4, no. 3, 2016, pp. 212-2.
Vancouver Gadain HE. Coupled singular and non singular thermoelastic system and Double Laplace Decomposition method. New Trends in Mathematical Sciences. 2016;4(3):212-2.
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