Exponential difference schemes with double integral transformation for solving convection-diffusion equations

被引：3

作者：

Polyakov S.V. ^{[1
]}

机构：

[1] Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow

来源：

Mathematical Models and Computer Simulations | 2013年 / 5卷 / 4期

关键词：

convection-diffusion equation; difference schemes; integral transformations; non-monotonic sweep algorithm;

D O I：

10.1134/S2070048213040121

中图分类号：

学科分类号：

摘要：

Convection-diffusion equations are studied. These equations are used for describing many nonlinear processes in solids, liquids, and gases. Although many works deal with solving them, they are still challenging in terms of theoretical and numerical analysis. In this work, the grid approach based on the method of finite differences for solving equations of this kind is considered. In order to make it easier, the one-dimensional version of such an equation was chosen. However, the equation preserves its principal properties; i.e., it is non-monotonic and non-linear. To solve boundary-value problems for such equations, a special variant of the non-monotonic sweep procedure is proposed. © 2013, Pleiades Publishing, Ltd.

引用

页码：338 / 340

页数：2

共 10 条

[1]

Samarskii A.A., Mikhailov A.P., Mathematical Simulation, (1997)

[2]

Samarskii A.A., On monotone difference schemes for elliptic and parabolic equations in the case of a non-self-adjoint elliptic operator, Zh. Vychislit. Matem. Matem. Fiz., 5, pp. 548-551, (1965)

[3]

Golant E.I., On self-adjoint families of difference schemes for parabolic equations with junior terms, Zh. Vychislit. Matem. Matem. Fiz., 18, pp. 1162-1169, (1978)

[4]

Karetkina N.V., An unconditionally stable difference scheme for parabolic equations with rst derivatives, Zh. Vychislit. Matem. Matem. Fiz., 20, pp. 236-240, (1980)

[5]

Fryazinov I.V., Balance method and variational-difference schemes, Dif. Uravn., 16, pp. 1332-1343, (1980)

[6]

Polyakov S.V., Sablikov V.A., Light-induced charge carriers lateral transfer in heterostructures with 2D electron gas, Matem. Model., 9, 12, pp. 76-86, (1997)

[7]

Kudryashova T.A., Polyakov S.V., On some methods of solving boundary-value problems on multiprocessor computers, Proceedings of the 4th International conference on mathematical simulation, June 27–July 1, 2000, Moscow, (2001)

[8]

Polyakov S.V., Exponential schemes for solving evolutionary equations on non-regular grids, Scientific Notes of Kazan State University, Physics and Mathematics, 149, pp. 121-131, (2007)

[9]

Karamzin Y.N., Polyakov S.V., Exponential finite volume schemes for solving elliptic and parabolic equations of the general type on non-regular grids, Grid Methods for Boundary-Value Problems and Applications. Proceedings of the 8th All-Russian Conference celebrating 80 anniversary of A. D. Lyashko, pp. 234-248, (2010)

[10]

Samarskii A.A., The Theory of Difference Schemes, (1971)

← 1 →