ABSTRACT
Turing's model is a model contains reaction-diffusion equation that capable to form skin patterns on an animal. In this paper, Turing's model was investigated, with the model improvisation by Barrio et al. [12], in parallel programming to shown its speed up impact. The parallel programming managed to speed up the process up to 8.9 times while retaining the quality of the result, compared to traditional programming.
- A. M. Turing. 1952. The Chemical Basis of Morphogenesis. Philos. Trans. R. Soc. Lond, Ser. B. Biol. Vol. 237, No. 641 (Aug. 1952), 37-72. https://doi.org/10.1098/rstb.1952.0012Google Scholar
- L. M. McNamara. 2017. Comprehensive Biomaterials II, 2.10 Bone as a Material, 202-227. Elsevier. https://doi.org/10.1016/B978-0-12-803581-8.10127-4Google Scholar
- T. Sekimura, A. Madzvamuse, A. J. Wathen, and P. K. Maini, 2000. A model for colour pattern formation in the butterfly wing of Papilio Dardanus. In Proceedings of the Royal Society B Biological Sciences, 7 May, 2000, London, Royal Society. https://doi.org/10.1098/rspb.2000.1081Google Scholar
- F. Shakeri and M. Dehghan. 2011. The finite volume spectral element method to solve Turing models in the biological pattern formation. Comput. Math. With Appl. 62, 12 (Dec. 2011), 4322-4336 https://doi.org/10.1016/j.camwa.2011.09.049Google ScholarDigital Library
- A. Madzvamuse, A. J. Wathen, P. K. Maini, 2003. A moving grid finite element method applied to a model biological pattern generator. J. Comput. Phys. 190, 2 (Sept. 2003), 478-500. https://doi.org/10.1016/S0021-9991(03)00294-8Google ScholarDigital Library
- J. Zhu, Y. -T. Zhang, S. A. Newman, M. Alber, 2009. Application of discontinuous Galerkin methods for reaction-diffusion systems in developmental biology. J. Sci, Comput. 40, (July 2009), 391-418. https://doi.org/10.1007/s10915-008-9218-4Google ScholarDigital Library
- R. T. Liu, S. S. Liaw, and P. K. Maini, 2005. Two-stage Turing model for generating pigment patterns on the leopard and the jaguar. Phys. Rev. E 74, 1, 011914 (July 2006). https://doi.org/10.1103/PhysRevE.74.011914Google ScholarCross Ref
- J. H. E. Cartwright. 2001. Labyrinthine Turing Pattern Formation in the Cerebral Cortex. J. Theor. Biol. 217, 1 (March 2002), 97-103. https://doi.org/10.1006/jtbi.2002.3012Google Scholar
- H. Kim, A. Yun, S. Yoon, C. Lee, J. Park, J. Kim, 2020. Pattern formation in reaction-diffusion systems on evolving surfaces. Comput. Math. With Appl. 80, 9 (Nov. 2020), 2019-2028. https://doi.org/10.1016/j.camwa.2020.08.026Google ScholarCross Ref
- S. A. Sarra. 2012. A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains. App. Math. And Comp. 218 (2012), 9853-9865. https://doi.org/10.1016/j.amc.2012.03.062Google ScholarCross Ref
- M. W. Smiley. 2008. An efficient implementation of a numerical method for a chemotaxis system. J. Comput. Math. 86, 2 (Dec. 2008), 219-235. https://doi.org/10.1080/00207160701864475Google ScholarDigital Library
- R. A. Barrio, C. Varea, J. L. Aragon, 1999. A Two-dimensional Numerical Study of Spatial Pattern Formation in Interacting Turing Systems. Bull. Math. Biol. 61, (May 1999), 483-505. https://doi.org/10.1006/bulm.1998.0093Google ScholarCross Ref
- W. L. Allen, I. C. Cuthill, N. E. Scott-Samuel, R. Baddeley, 2010. Why the leopard got its spot: relating pattern development to ecology in felids. In Proceedings of the Royal Society B Biological Sciences, 20 Oct. 2010, London, Royal Society. https://doi.org/10.1098/rspb.2010.1734Google Scholar
- J. C. Butcher. 2008. Numerical Methods for Ordinary Differential Equations (2nd. Ed.). John Wiley & Sons, Chichester, West Sussex, UK.Google Scholar
- A. H. Workie. 2020. New Modification on Heun's Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency. J. Math. 2020, Article 6650855 (Dec. 2020). https://doi.org/10.1155/2020/6650855Google Scholar
- J. Cheng, M. Grossman, T. McKercher, 2014. Professional CUDA C Programming. John Wiley & Sons, Indianapolis, Indiana, US.Google Scholar
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