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

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  • Cveticanin, L.

Abstract

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

Suggested Citation

  • Cveticanin, L., 2009. "Application of homotopy-perturbation to non-linear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 221-228.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:221-228
    DOI: 10.1016/j.chaos.2007.07.053
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    References listed on IDEAS

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    1. Odibat, Zaid & Momani, Shaher, 2008. "Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 167-174.
    2. Wang, Qi, 2008. "Homotopy perturbation method for fractional KdV-Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 843-850.
    3. Abbasbandy, S., 2007. "Application of He’s homotopy perturbation method to functional integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1243-1247.
    4. Golbabai, A. & Keramati, B., 2008. "Modified homotopy perturbation method for solving Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1528-1537.
    5. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    6. Tan, Yue & Xu, Hang & Liao, Shi-Jun, 2007. "Explicit series solution of travelling waves with a front of Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 462-472.
    7. Cveticanin, L., 2006. "Homotopy–perturbation method for pure nonlinear differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1221-1230.
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