﻿ 变系数2D对流扩散方程的高阶迭代算子分裂方法

# 变系数2D对流扩散方程的高阶迭代算子分裂方法Higher Order Iterative Operator Splitting Method for the 2D Convection Diffusion Equation with Variable Coefficients

Abstract: In this paper, a novel higher order iterative operator splitting method is presented for the 2D convection diffusion equation with the variable coefficient. The proposed scheme combines the classical iterative scheme and Zassenhaus product formula for the temporal discretization. And Fourier pseudo spectral method and dimensional splitting scheme are applied for the spatial operators. The numerical results verified that the proposed method can get second order accuracy by weighted iterative scheme. Besides, the new method not only can reduce numerical error but also save a lot of CPU time than the classical iterative method.

[1] 章本照, 印建安, 张宏基. 流体力学数值方法[M]. 北京: 机械工业出版社, 2003

[2] 李荣华, 刘播. 微分方程数值解法[M]. 第四版. 北京: 高等教育出版社, 2009.

[3] Li, Q., Chai, Z. and Shi, B. (2014) An Efficient Lattice Boltzmann Model for Steady Convection Diffusion Equation. Journal of Scientific Computing, 61, 308-326.
https://doi.org/10.1007/s10915-014-9827-z

[4] Galligani, E. (2013) A Nonlinearity Lagging for the Solution of Nonlinear Steady State Reaction Diffusion Problems. Communications in Nonlinear Science and Numerical Simulation, 18, 567-583.

[5] Angelini, O. and Brenner, K. (2013) A Finite Volume Method on General Meshes for a Degenerate Parabolic Convection Reaction Diffusion Equation. Numerische Mathematik, 123, 219-257.
https://doi.org/10.1007/s00211-012-0485-5

[6] Bause, M. and Schwegler, K. (2013) Higher Order Finite Element Approximation of Systems of the Convection Diffusion Reaction Equations with Small Diffusion. Journal of Computational and Applied Mathematics, 246, 52-64.

[7] Geiser, J. and Tanoglu, G. (2011) Operator-Splitting Methods via the Zassenhaus Product Formula. Applied Mathematics and Computation, 217, 4557-4575.

[8] Csomós, P. and Faragó, I. (2005) The Weighted Sequential Splitting and Their Analysis. Computers and Mathematics with Applications, 50, 1017-1031.

[9] Geiser, J. (2008) Iterative Operator-Splitting Methods with Higher-Order Time Integration Methods and Applications for Parabolic Partial Differential Equations. Journal of Computational Applied Mathematics, 217, 227-242.
https://doi.org/10.1002/num.20568

[10] Geiser, J. (2011) Iterative Operator-Splitting Methods for the Nonlinear Differential Equations and Applications. Numerical Method for Partial Differential Equation, 27, 1026-1054.

[11] Shen, J., Tang, T. and Wang, L. (2011) Spectral Methods. Springer, Berlin Heidelberg.
https://doi.org/10.1007/978-3-540-71041-7

[12] Scholz, D. (2006) A Note on the Zassenhaus Product Formula. Journal of Mathematical Physics, 47, 373-418.
https://doi.org/10.1063/1.2178586

[13] Geiser, J. and Tano, G. (2011) Higher Order Operator Splitting Methods via the Zassenhaus Product Formula: Theory and Application. Computer and Mathematic with Application, 62, 1994-2015.

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