Application of homotopy-perturbation to non-linear partial differential equations

作者: L. Cveticanin

DOI: 10.1016/J.CHAOS.2007.07.053

关键词: First-order partial differential equationMethod of characteristicsPartial differential equationHomotopy analysis methodMathematical analysisStochastic partial differential equationLinear differential equationMathematicsDifferential equationNumerical partial differential equationsGeneral Mathematics

摘要: Abstract In this paper He’s homotopy perturbation method has been adopted for solving non-linear partial differential equations. An approximate solution of the equation which describes longitudinal vibration a beam is obtained. The compared with that found using variational iteration introduced by He. difference between two solutions negligible.

参考文章(36)
Ji-Huan He, Approximate analytical solution for seepage flow with fractional derivatives in porous media Computer Methods in Applied Mechanics and Engineering. ,vol. 167, pp. 57- 68 ,(1998) , 10.1016/S0045-7825(98)00108-X
Ji-Huan He, Approximate solution of nonlinear differential equations with convolution product nonlinearities Computer Methods in Applied Mechanics and Engineering. ,vol. 167, pp. 69- 73 ,(1998) , 10.1016/S0045-7825(98)00109-1
A. H. Nayfeh, S. A. Nayfeh, Nonlinear Normal Modes of a Continuous System With Quadratic Nonlinearities Journal of Vibration and Acoustics. ,vol. 117, pp. 199- 205 ,(1995) , 10.1115/1.2873898
Ji-Huan He, Variational iteration method – a kind of non-linear analytical technique: some examples International Journal of Non-linear Mechanics. ,vol. 34, pp. 699- 708 ,(1999) , 10.1016/S0020-7462(98)00048-1
W. Lacarbonara, DIRECT TREATMENT AND DISCRETIZATIONS OF NON-LINEAR SPATIALLY CONTINUOUS SYSTEMS Journal of Sound and Vibration. ,vol. 221, pp. 849- 866 ,(1999) , 10.1006/JSVI.1998.2049
S. W. Shaw, An invariant manifold approach to nonlinear normal modes of oscillation Journal of Nonlinear Science. ,vol. 4, pp. 419- 448 ,(1994) , 10.1007/BF02430640
Guoping Pang, Fengyan Wang, Lansun Chen, Analysis of a Monod–Haldene type food chain chemostat with periodically varying substrate Chaos, Solitons & Fractals. ,vol. 38, pp. 731- 742 ,(2008) , 10.1016/J.CHAOS.2007.01.018
Ji-Huan He, The homotopy perturbation method for nonlinear oscillators with discontinuities Applied Mathematics and Computation. ,vol. 151, pp. 287- 292 ,(2004) , 10.1016/S0096-3003(03)00341-2
Qi Wang, Homotopy perturbation method for fractional KdV-Burgers equation Chaos Solitons & Fractals. ,vol. 35, pp. 843- 850 ,(2008) , 10.1016/J.CHAOS.2006.05.074