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A New Stable Algorithm for Fractional Navier–Stokes Equation in Polar Coordinate

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Abstract

This paper presents a new approximate method based on operational matrices of fractional integrations and differentiations for fractional Navier–Stokes equation in polar coordinate system using Legendre scaling functions as a basis. Convergence analysis as well as error analysis of the proposed methods is given. Numerical stability of the method is shown. Numerical examples are given to show the effectiveness of the proposed method. Results are compared with existing analytical methods to show the accuracy of the proposed method.

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Acknowledgements

The author is very grateful to the referees for their constructive comments and suggestions for the improvement of the paper.

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  1. Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi, 221005, India

    Harendra Singh

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  1. Harendra Singh
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Singh, H. A New Stable Algorithm for Fractional Navier–Stokes Equation in Polar Coordinate. Int. J. Appl. Comput. Math 3, 3705–3722 (2017). https://doi.org/10.1007/s40819-017-0323-7

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  • DOI: https://doi.org/10.1007/s40819-017-0323-7

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