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Numerical solutions of time-fractional coupled viscous Burgers’ equations using meshfree spectral method

  • Manzoor Hussain
  • Sirajul HaqEmail author
  • Abdul Ghafoor
  • Ihteram Ali
Article
  • 28 Downloads

Abstract

In this article, we compute numerical solutions of time-fractional coupled viscous Burgers’ equations using meshfree spectral method. Radial basis functions (RBFs) and spectral collocation approach are used for approximation of the spatial part. Temporal fractional part is approximated via finite differences and quadrature rule. Approximation quality and efficiency of the method are assessed using discrete \(E_{2}\), \(E_{\infty }\) and \(E_{\text {rms}}\) error norms. Varying the number of nodal points M and time step-size \(\Delta t\), convergence in space and time is numerically studied. The stability of the current method is also discussed, which is an important part of this paper.

Keywords

Coupled Burgers’ equations Meshfree spectral method Radial basis functions Caputo fractional derivative Shape parameter 

Mathematics Subject Classification

65M70 

Notes

Acknowledgements

The authors are grateful to the anonymous reviewers for their valuable suggestions which improved the quality of the work.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  • Manzoor Hussain
    • 1
  • Sirajul Haq
    • 1
    Email author
  • Abdul Ghafoor
    • 1
  • Ihteram Ali
    • 1
  1. 1.Faculty of Engineering SciencesGIK InstituteTopiPakistan

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