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A meshless collocation method based on Pascal polynomial approximation and implicit closest point method for solving reaction–diffusion systems on surfaces

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Abstract

A local meshless collocation method has been designed for solving reaction–diffusion systems on surfaces. The proposed numerical procedure is based on Pascal polynomial approximation and closest point method. This method is geometrically flexible and can be applied to solving partial differential equations on unstructured point clouds. It only needs a set of arbitrarily scattered mesh-free points representing the underlying surface.

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Acknowledgements

We thank the three reviewers very much for putting time and energy to investigate the initial manuscript and providing many fruitful recommendations that really helped us to improve the quality of the present article.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology(Tehran Polytechnic), No. 424, Hafez Ave., Tehran, 15914, Iran

    Hasan Zamani-Gharaghoshi, Mehdi Dehghan & Mostafa Abbaszadeh

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  1. Hasan Zamani-Gharaghoshi
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  2. Mehdi Dehghan
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  3. Mostafa Abbaszadeh
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Correspondence to Mehdi Dehghan.

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Zamani-Gharaghoshi, H., Dehghan, M. & Abbaszadeh, M. A meshless collocation method based on Pascal polynomial approximation and implicit closest point method for solving reaction–diffusion systems on surfaces. Engineering with Computers 40, 313–322 (2024). https://doi.org/10.1007/s00366-023-01794-y

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