Identification of HPM and ADM for the (n+1)-dimensional Equal Width Wave
Equation with Diffusion and Damping term

R. Asokan; E. Nakkeeran; T. Shanmuga Priya

doi:https://doi.org/10.14445/22315373/IJMTT-V56P551

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 6 | Year 2018 | Article Id. IJMTT-V56P551 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P551

Identification of HPM and ADM for the (n+1)-dimensional Equal Width Wave Equation with Diffusion and Damping term

R. Asokan, E. Nakkeeran, T. Shanmuga Priya

Citation :

R. Asokan, E. Nakkeeran, T. Shanmuga Priya, "Identification of HPM and ADM for the (n+1)-dimensional Equal Width Wave Equation with Diffusion and Damping term," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 6, pp. 380-391, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P551

Abstract

In this paper, We present the homotopy perturbation method (HPM) and Adomian Decomposition Method (ADM) to obtain a closed form solution of the (n+1)-dimensional Equal Width wave equation with diffusion and dispersion term. These methods consider the use of the initial or boundary conditions and find the solution without any discretization, transformation or restrictive conditions and avoid the round-off errors. Few numerical examples are provided to validate the reliability and efficiency of the three methods.

Keywords

Nonlinear PDE,Adomian Decomposition Method,Differential transform method,and homotopy perturbation method.

References

1. Z. Odibat, S. Momani, Chaos Solitons Fractals, in press.
2. J.H. He, Comput. Methods Appl. Mech. Engrg. 178,(1999),257.
3. J.H. He, Int. J. Non-Linear Mech., 35 (1), (2000), 37.
4. M. El-Shahed, Int. J. Nonlin. Sci. Numer. Simul., 6 (2),(2005),163.
5. J.H. He, Appl. Math. Comput., 151, (2004), 287.
6. J.H. He, Int. J. Nonlin. Sci. Numer. Simul., 6 (2),(2005),207.
7. J.H. He, Phys. Lett. A ,374, (4-6), (2005), 228.
8. J.H. He, Chaos Solitons Fractals, 26 (3), (2005), 695.
9. J.H. He, Phys. Lett. A, 350, (1-2), (2006), 87.
10. J.H. He,Appl. Math. Comput., 135, (2003), 73.
11. J.H. He, Appl. Math. Comput.,156, (2004), 527.
12. J.H. He, Appl. Math. Comput., 156,(2004), 591.
13. J.H. He, Chaos Solitons Fractals, 26, (3), (2005), 827. 11
14. A. Siddiqui, R. Mahmood, Q. Ghori, Int. J. Nonlin. Sci. Numer. Simul., 7 (1), (2006), 7.
15. A. Siddiqui, M. Ahmed, Q. Ghori, Int. J. Nonlin. Sci. Numer. Simul., 7 (1), (2006), 15.
16. J.H. He, Int. J. Mod. Phys. B, 20 (10), (2006), 1141.
17. S. Abbasbandy, Appl. Math. Comput., 172, (2006), 485.
18. S. Abbasbandy, Appl. Math. Comput., 173, (2006), 493.
19. S.Padmasekaran and S.Rajeswari,Solitons and Exponential Solutions for a Nonlinear (2+1)dim PDE, IJPAM,Volume 115 No. 9 2017, 121-130.
20. S. Padmasekaran and S. Rajeswari, Lies Symmetries of (2+1)dim PDEIJMTT,Volume 51 No. 6,11-2017.
21. S. Padmasekaran and S. Rajeswari, Solution of Semilinear Parabolic Equations with Vari- able Coefficients
22. G. Adomian. A review of the decomposition method in applied mathematics., J Math Anal Appl, (1988), 135, 501-544.
23. F.J. Alexander, J.L. Lebowitz . Driven diffusive systems with a moving obstacle: a variation on the Brazil nuts problem. J Phys (1990), 23, 375-382.
24. F.J. Alexander, J.L. Lebowitz.,On the drift and diffusion of a rod in a lattice uid. J Phys, (1994), 27, 683-696.
25. J.D. Cole., On a quasilinear parabolic equation occurring in aerodynamics. J Math Appl, (1988), 135, 501-544.
26. He J.H. Homotopy perturbation technique. Comput Methods Appl Mech Eng, (1999), 178, 257-262.
27. J.H. He.,Homotopy perturbation method: a new nonlinear analytical technique., Appl Math Comput, (2003), 13, (2-3), 73-79.
28. J.H. He.,A simple perturbation method to Blasius equation. Appl Math Comput, (2003), (2-3), 217-222.
29. Morrison, P. J., Meiss, J. D., Carey, J. R.: Scattering of RLW solitary waves, Physica D 11 ,(1984), 324-336.