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He‐Laplace Method for Linear and Nonlinear Partial Differential Equations

Author

Listed:
  • Hradyesh Kumar Mishra
  • Atulya K. Nagar

Abstract

A new treatment for homotopy perturbation method is introduced. The new treatment is called He‐Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the proposed scheme provides the solution without any discretization or restrictive assumptions and avoids the round‐off errors.

Suggested Citation

  • Hradyesh Kumar Mishra & Atulya K. Nagar, 2012. "He‐Laplace Method for Linear and Nonlinear Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:180315
    DOI: 10.1155/2012/180315
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    References listed on IDEAS

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    1. Biazar, J. & Ghazvini, H., 2009. "He’s homotopy perturbation method for solving systems of Volterra integral equations of the second kind," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 770-777.
    2. Ghorbani, Asghar, 2009. "Beyond Adomian polynomials: He polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1486-1492.
    3. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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    Cited by:

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    2. Sabir Widatalla & M. Z. Liu, 2013. "New Iterative Method Based on Laplace Decomposition Algorithm," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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