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Russia Zelenograd
Section  Mathematics 
Title  A new approach to the reactiondiffusion systems modelling 
Author(s)  Nazarov M.N.^{a} 
Affiliations  National Research University of Electronic Technology^{a} 
Abstract  We consider a new technique for modelling the reactiondiffusion systems based on systems of ordinary differential equations. In contrary to the specialized numerical methods such as straight line method, this new technique is positioned at model level as a full alternative for partial differential equations. The description of this new method is quite similar to the description of finite volume method, except that it uses statistical simplifications and principles of geometric probability to describe diffusion processes. The main goal of this approach is to simplify the qualitative analysis of reactiondiffusion systems and to increase the efficiency of the numerical implementation. The first task is successfully resolved because of the fact that for the qualitative analysis of model dynamics based on ordinary differential equations it is possible to use the apparatus of the classical theory of dynamical systems. The second task is solved only partially, because the gain in efficiency while maintaining acceptable accuracy for numerical implementation will be considerable only for certain simple initial distribution of molecules, as well as for certain diffusion coefficients. To determine the criteria for practical application of this technique we also estimate the model error in general. 
Keywords  reactiondiffusion, alternative to partial derivatives, dynamic systems theory 
UDC  517.958 
MSC  35K57, 76R50 
DOI  10.20537/vm140407 
Received  23 September 2014 
Language  Russian 
Citation  Nazarov M.N. A new approach to the reactiondiffusion systems modelling, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 4, pp. 8494. 
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