论文信息 - An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations

An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations

We discuss an efficient higher order finite difference algorithm for solving systems of 3-D reaction-diffusion equations with nonlinear reaction terms. The algorithm is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular seven-point difference stencil similar to that used in the standard second-order algorithms, such as the Crank-Nicolson algorithm. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.

[1] A. R. Mitchell,et al. The Finite Difference Method in Partial Differential Equations , 1980 .

[2] Y. Adam,et al. Highly accurate compact implicit methods and boundary conditions , 1977 .

[3] Ayodeji O. Demuren,et al. Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows , 1998 .

[4] R. Hirsh,et al. Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique , 1975 .

[5] J. J. Douglas. On the Numerical Integration of $\frac{\partial ^2 u}{\partial x^2 } + \frac{\partial ^2 u}{\partial y^2 } = \frac{\partial u}{\partial t}$ by Implicit Methods , 1955 .

[6] H. Kreiss,et al. Time-Dependent Problems and Difference Methods , 1996 .

[7] H. H. Rachford,et al. The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[8] Juan I. Ramos. Implicit, compact, linearized θ-methods with factorization for multidimensional reaction-diffusion equations , 1998, Appl. Math. Comput..

[9] Jianping Zhu,et al. An efficient high‐order algorithm for solving systems of reaction‐diffusion equations , 2002 .

[10] S. Lele. Compact finite difference schemes with spectral-like resolution , 1992 .