Институт вычислительной математики и математической геофизики СОРАН

Abstracts

numerical solution of DE and IE

Here we present semi-implicit difference shemes for integration of autonimous differential equation systems that stand for gene network models proposed by Institute of cytology and genetics SB RAS, e.g. model of substance synthesis, model of auxin distribution in plants root.

The autonomic systems describe processes of diffusion and substance convey in one dimensional way. This feature allows to use special type of right side and propose efficient semi-implicit difference schemes with first order of approximation. At each step of integration it is one time required the solving of linear algebraic equations system with three diagonal monotonous matrix that takes the major part of computational time without considering time for computing of matrix elements. At the end of each step it is required the solving of one non-linear scalar equation [1].

As a rule considered autonomous systems are big dimensional thus such a special integration method is demanded. For example, in models of multistage substance synthesis the number of equations depends on number of stages and can get several millions. The proposed economic algorithm allows to study numerically the limiting properties of solution of autonomous systems using regular computers. While modeling processes in a plant root the dimension of a system is determined by the number of cells.

The developed algorithms are presented in the "HGNET-S" package. The package performance is demonstrated.

[1] Fadeev S.I., Likhoshvai V.A., Shtokalo D.N., Korolev V.K. Studying the mathematical models for the matrix synthesis of non-regular polymers of DNA, RNA and proteins // Siberian electronic mathematical reports, 2010. Vol. 7, pp. 467-475.

Note. Abstracts are published in author's edition

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