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Improved wavelets based technique for nonlinear partial differential equations

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Abstract

One of the most challenging task now a days for engineers and scientists is finding solutions of nonlinear Partial Differential Equations (PDEs) which frequently arise in many engineering and physical phenomena’s. Encouraged by the ongoing research, a new technique is proposed in this article for obtaining more accurate results of nonlinear PDEs. Shifted Legendre wavelets and Picard’s Iteration Technique are used in the proposed technique. To test the significance of the proposed technique, nonlinear Gardner equation is considered and solved. The proposed technique provides very accurate results over a wider interval because of the use of the shifted polynomials. The results obtained are also compared with the results of Variational Iteration Method and the supremacy of the proposed method is established.

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Acknowledgements

The authors are highly grateful to the unknown referees for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, MohiUd Din Islamic University, Nerian Sharif, AJ&K, Pakistan

    Muhammad Asad Iqbal & Muhammad Shakeel

  2. Department of Mathematics, Institute of Southern Punjab, Multan Campus, Multan, Pakistan

    Ayyaz Ali

  3. Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, Pakistan

    Syed Tauseef Mohyud-Din

Authors
  1. Muhammad Asad Iqbal
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  2. Muhammad Shakeel
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  3. Ayyaz Ali
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  4. Syed Tauseef Mohyud-Din
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Correspondence to Syed Tauseef Mohyud-Din.

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Iqbal, M.A., Shakeel, M., Ali, A. et al. Improved wavelets based technique for nonlinear partial differential equations. Opt Quant Electron 49, 167 (2017). https://doi.org/10.1007/s11082-017-1001-z

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  • DOI: https://doi.org/10.1007/s11082-017-1001-z

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