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Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations

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  • Fukang Yin
  • Junqiang Song
  • Xiaoqun Cao
  • Fengshun Lu

Abstract

This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.

Suggested Citation

  • Fukang Yin & Junqiang Song & Xiaoqun Cao & Fengshun Lu, 2013. "Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, February.
    • Handle: RePEc:hin:jnljam:157956
    DOI: 10.1155/2013/157956
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    Cited by:

    1. Reza Doostaki & Mohammad Mehdi Hosseini, 2022. "Option Pricing by the Legendre Wavelets Method," Computational Economics, Springer;Society for Computational Economics, vol. 59(2), pages 749-773, February.

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