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.
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The authors are grateful to the anonymous reviewers for their valuable suggestions which improved the quality of the work.
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Communicated by José Tenreiro Machado.
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Hussain, M., Haq, S., Ghafoor, A. et al. Numerical solutions of time-fractional coupled viscous Burgers’ equations using meshfree spectral method. Comp. Appl. Math. 39, 6 (2020). https://doi.org/10.1007/s40314-019-0985-3
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DOI: https://doi.org/10.1007/s40314-019-0985-3
Keywords
- Coupled Burgers’ equations
- Meshfree spectral method
- Radial basis functions
- Caputo fractional derivative
- Shape parameter