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A cubic B-spline quasi-interpolation algorithm to capture the pattern formation of coupled reaction-diffusion models

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Abstract

Diffusion plays a significant role in complex pattern formulations occurred in biological and chemical reactions. In this work, the authors study the effect of diffusion in coupled reaction-diffusion systems named the Gray-Scott model for complex pattern formation with the help of cubic B-spline quasi-interpolation (CBSQI) method and capture various formates of these patterns. The idea of Kronecker product is used first time with CBSQI method for 2D problems. Linear stability analysis of the reaction-diffusion system as well as stability of the proposed method is studied. Four test problems are considered to check the accuracy and efficiency of the method and found the stable patterns.

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Acknowledgements

The author Sudhir Kumar would like to thank Council of Scientific and Industrial Research (CSIR), Government of India (File no: 09/143(0889)/2017-EMR-I).

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Authors and Affiliations

  1. Department of Mathematics, Jaypee Institute of Information Technology Noida, Noida, India

    R. C. Mittal

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Sudhir Kumar & Ram Jiwari

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  1. R. C. Mittal
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  2. Sudhir Kumar
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  3. Ram Jiwari
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Correspondence to Sudhir Kumar.

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Mittal, R.C., Kumar, S. & Jiwari, R. A cubic B-spline quasi-interpolation algorithm to capture the pattern formation of coupled reaction-diffusion models. Engineering with Computers 38 (Suppl 2), 1375–1391 (2022). https://doi.org/10.1007/s00366-020-01278-3

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