Improved wavelets based technique for nonlinear partial differential equations

  • Muhammad Asad Iqbal
  • Muhammad Shakeel
  • Ayyaz Ali
  • Syed Tauseef Mohyud-Din


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.


Shifted Legendre wavelets Picard’s iteration Nonlinear problems Exact solutions 



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

Compliance with ethical standards

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this paper.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Muhammad Asad Iqbal
    • 1
  • Muhammad Shakeel
    • 1
  • Ayyaz Ali
    • 2
  • Syed Tauseef Mohyud-Din
    • 3
  1. 1.Department of MathematicsMohiUd Din Islamic UniversityNerian SharifPakistan
  2. 2.Department of MathematicsInstitute of Southern PunjabMultanPakistan
  3. 3.Department of Mathematics, Faculty of SciencesHITEC UniversityTaxilaPakistan

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