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A novel approach for multi dimensional fractional coupled Navier–Stokes equation

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Abstract

This study proposed a new scheme called the Hermite wavelet method (HWM) to find the numerical solutions to the multidimensional fractional coupled Navier–Stokes equation (NSE). This approach is based on the Hermite wavelets approximation with collocation points. Here, we reduce the fractional NSE into a set of nonlinear algebraic equations involving Hermite wavelet unknown coefficients. Convergence analysis is explained through the theorems. Three examples are given to validate the proposed technique’s efficiency and discussed the comparison between the present method solutions with the exact solution. The obtained results are represented through graphs and tables for both integer and fractional order. These results disclose that the existing algorithm offers a better result.

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Acknowledgements

The author expresses his affectionate thanks to the respected Editor in chief and honourable reviewers for their valuable suggestions and comments to improve the presentation of this article. It is a pleasure to thank the University Grants Commission (UGC), Govt. of India for the financial support under UGC-BSR Research Start Up Grant for 2021-2024:F.30-580/2021(BSR) Dated: 23rd Nov. 2021.

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  1. Department of Mathematics, Bangalore University, Bengaluru, 560056, India

    S. Kumbinarasaiah

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Kumbinarasaiah, S. A novel approach for multi dimensional fractional coupled Navier–Stokes equation. SeMA 80, 261–282 (2023). https://doi.org/10.1007/s40324-022-00289-y

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