Solving Inhomogeneous Wave Equation Cauchy Problems using Homotopy Perturbation Method

In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).

• Mohamed M. Mousa
• Aidarkhan Kaltayev

• Homotopy perturbation method
• Exact solution
• Cauchy problem
• inhomogeneous wave equation

[1] J.H. He, Homotopy perturbation technique, Comput. Methods Appl.
Mech. Eng., vol. 178, pp. 257-262, 1999.
[2] J.H. He, Homotopy perturbation method: a new nonlinear analytical
technique, Appl. Math. Comput., vol. 135, pp. 73-79, 2003.
[3] J.H. He, Comparison of homotopy perturbation method and homotopy
analysis method, Appl. Math. Comput., vol. 156, pp. 527-539, 2004.
[4] J.H. He, Application of homotopy perturbation method to nonlinear
wave equations, Chaos, Solitons Fractals, vol. 26, pp. 695-700, 2005.
[5] Q.K. Ghori, M. Ahmed and A.M. Siddiqui, Application of homotopy
perturbation method to squeezing flow of a Newtonian fluid, Int. J.
Nonlinear Sci. Numer. Simul., vol. 8(2), pp. 179-184, 2007.
[6] T. Ozis and A. Yildirim, A comparative study of He's homotopy
perturbation method for determining frequency-amplitude relation of a
nonlinear oscillator with discontinuities, Int. J. Nonlinear Sci. Numer.
Simul., vol. 8(2), pp. 243-248, 2007.
[7] S.J. Li and Y.X. Liu, An improved approach to nonlinear dynamical
system identification using PID neural networks, Int. J. Nonlinear Sci.
Numer. Simul., vol. 7(2), pp. 177-182, 2006.
[8] M.M. Mousa and S.F. Ragab, Application of the homotopy perturbation
method to linear and nonlinear schrödinger equations, Z.Naturforsch.
vol. 63a, pp. 140-144, 2008.
[9] Dean G. Duffy, Advanced engineering mathematics, CRC press, New
York, 1997.