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Modified Chebyshev Wavelet-Picard Technique for Thin Film Flow of Non-Newtonian Fluid Down an Inclined Plane

  • Muhammad Asad Iqbal
  • Umar Khan
  • Ayyaz Ali
  • Syed Tauseef Mohyud-Din
Research Article
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Abstract

For the past few decades, solutions of the nonlinear differential equations are of great importance and interest for researchers and scientists around the globe. Most of the physical phenomena’s around us can easily be modeled into nonlinear differential equations. In this article, a new method is proposed by using shifted Chebyshev wavelets and Picard iteration technique to tackle with the nonlinearity of these physical problems. The proposed scheme is very user friendly and extremely accurate. The accuracy of the proposed scheme is verified by the help of a nonlinear physical model representing the thin film flow of a third grade fluid down an inclined plane. Numerical solution is also sought using Runge–Kutta order 4 method. Results are obtained by shifted Chebyshev wavelets at different iterations of Picard technique for different values of parameters are described in table and graphs which confirms the accuracy and stability of the proposed technique.

Keywords

Thin film flow Chebyshev wavelets method Picard iteration technique Numerical solution 

Mathematics Subject Classification

35Q79 42C15 39B9 

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Copyright information

© The National Academy of Sciences, India 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe University of Poonch RawalakotRawalakotPakistan
  2. 2.Department of MathematicsCOMSATS Institute of Information TechnologyAbbottabadPakistan
  3. 3.Department of Mathematics, Faculty of SciencesHITEC UniversityTaxilaPakistan
  4. 4.Center for Research (CFR)University of Islamabad (UoI)IslamabadPakistan

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