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Numerical simulations of reaction–diffusion systems in biological and chemical mechanisms with quartic-trigonometric B-splines

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Abstract

This article concerns with the numerical investigations of the reaction–diffusion systems (RDSs) arising in the study of pattern formation in biological and chemical systems with the employment of the quartic-trigonometric B-spline functions. The computationally numerical scheme uses collocation method which is established by a relatively new B-splines for the spatial discretizations and, for time integration Crank–Nicolson technique is adapted. Therefore, solutions of the RDSs are assembled by the wholly discretized space-time scheme. A matrix stability analysis is performed for the numerical scheme after linearization process. Experimental cases include Brusselator model, Gray–Scott model, Schnakenberg model as well as a linear problem in one-dimensional domain. Numerical solutions are compared to the existing studies. Spatial pattern formation is demonstrated by present computational algorithm.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science and Letters, Eskisehir Osmangazi University, Eskişehir, Turkey

    Ozlem Ersoy Hepson

  2. Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    Gülsemay Yiğit & Tofigh Allahviranloo

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  1. Ozlem Ersoy Hepson
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  2. Gülsemay Yiğit
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  3. Tofigh Allahviranloo
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All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, each author certifies that this material or similar material has not been and will not be submitted to or published in any other publication.

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Correspondence to Tofigh Allahviranloo.

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No conflict of interest exists. We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

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Communicated by Baisheng Yan.

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Hepson, O.E., Yiğit, G. & Allahviranloo, T. Numerical simulations of reaction–diffusion systems in biological and chemical mechanisms with quartic-trigonometric B-splines. Comp. Appl. Math. 40, 144 (2021). https://doi.org/10.1007/s40314-021-01524-4

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  • DOI: https://doi.org/10.1007/s40314-021-01524-4

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