International Scientific Journal

Thermal Science - Online First

online first only

Approximate analytical solution for one dimensional problems of thermoelasticity with dirichlet condition

This paper presents the solution of the initial boundary-value problem for the system of one-dimensional thermoelasticity using a new modified decomposition method that takes into accounts both initial and boundary conditions. The obtained solution is based on the generalized form of the inverse operator and is given in the form of a finite series. Also, some numerical experiments were presented to the both the effectiveness and the accuracy of the presented method.
PAPER REVISED: 2017-02-17
PAPER ACCEPTED: 2017-02-17
  1. Chen, Y. Q.,, A model of coupled thermosolutal convection and thermoelasticity in soft rocks with consideration of water vapor absorption, International Journal of Heat and Mass Transfer, 97 (2016), pp. 157-173
  2. Kakhki, E. K.,, An analytical solution for thermoelastic damping a micro-beam based on generalized theory of thermoelasticity and modified couple stress theory, Applied Mathematical Modling, 40 (2016), pp. 3164-3174
  3. Abd-Alla, A. N.,, Harmonic wave generation in nonlinear thermoelasticity, Int. J. Eng. sci. 32 (1994), pp. 1103-1110
  4. Rawy, E. K.,, Numerical solution for a nonlinear, one-dimensional problem of thermoelasticity, Journal of Computational and Applied Mathematics, 100 (1998), pp. 53-76
  5. Quintanilla, R., Convergence and structural stability in thermoelasticity, Applied Mathematics and Computation 135 (2003), pp. 287-300
  6. Copehi, M. I., French D.A., Numerical solutions of the stability of steady-state solutions to a contact problem in coupled thermoelasticity, Applied Mathematical Modeling 28 (2004), pp. 323-332.
  7. Rincon, M. A.,, Numerical method, existence and uniqueness for the thermoelasticity system with moving boundary, Computational and Applied Mathematics, 24 (2005), 3, pp. 439-460
  8. Almazmumy, M., decomposition method and series solutionsfor system of one-dimensional problems of thermoelasticity, , International Journal of Numerical Methods and Applications, 15(2) (2016), pp. 167-181
  9. Sweilam, N. H., Khader, M. M., Variational iteration method for one dimensional nonlinear thermoelasticity, Chaos, solitons and Fractals 32 (2007), pp. 145-149
  10. Khaldjigitov, A.,, Numerical solution of 1D and 2D thermoelastic coupled problems, International Journal of modern physics: conference series, 9 (2012), pp. 503-510
  11. Sweilam, N. H., Harmonic wave generation in nonlinear thermoelasticity by variational iteration method and Adomian's method, Journal of Computational and Applied Mathematics, 207 (2007), pp. 64-72
  12. Sadighi, A., Ganji, D. D., A study on one dimensional nonlinear thermoelasticity by Adomian decomposition method, World Journal of Modelling and Simulation, 4 (2008), 1, pp. 19-25
  13. Adomian, G., Nonlinear Stochastic systems and Applications to physics, Kluwer Academic Publishers, Dordrecht, 1989
  14. Adomian, G., Solving frontier problems of physics: the decomposition method, Kluwer Academic Publishers, Boston, 1994
  15. Wazwaz, A. M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. Math. and Comput, 111 (2000), 1, pp. 53-69
  16. Almazmumy, M., Decomposition method and Series Solutions for system of one- dimentional Problem of Thermoelasticity, International Journal of Numerical Methods and Applications. 15 (2016), 2, pp. 167-181
  17. Ebaid, A., A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method, J. Computational and Applied Mathematics, 235 (2011), pp. 1914-1924
  18. Chun, C.,, An approach for solving singular two-point boundary value problems: analytical and numerical treatment, Australian and New Zealand Industrial and Applied Mathematics Journal, 53E (2012), pp. 21-43