MONOTONE DIFFERENCE SCHEMES FOR THE SCHNACKENBERG MODEL
Abstract
In this article the canonical form of the vector-difference schemes is constructed. The definition of the monotonicity of difference schemes is given. This definition is related to the positivity property of the difference solution. Based on this definition, the monotone difference schemes for the Schnakenberg model with the Dirichlet and Neumann boundary
conditions are constructed. This model is a semi-nonlinear reaction-diffusion system, and it plays an important role in mathematical modeling in the fields of physical chemistry and biology. In constructing a monotone difference scheme for this model with the Neumann boundary condition, the idea of half-integral nodes at the boundary points under the secondkind boundary conditions is used. The results of numerical experiments have confirmed the effectiveness of the suggested methods. the numerical solution without nonphysical oscillation is obtained.
conditions are constructed. This model is a semi-nonlinear reaction-diffusion system, and it plays an important role in mathematical modeling in the fields of physical chemistry and biology. In constructing a monotone difference scheme for this model with the Neumann boundary condition, the idea of half-integral nodes at the boundary points under the secondkind boundary conditions is used. The results of numerical experiments have confirmed the effectiveness of the suggested methods. the numerical solution without nonphysical oscillation is obtained.
About the Author
Thi Kim Tuyen Vo
Belarusian State University, Hue Industrial College
Belarus
Postgraduate
Belarus
Postgraduate
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