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《Mathematica Numerica Sinica》 2005-02
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A COMPACT ALTERNATE DIRECT IMPLICIT DIFFERENCE METHOD FOR THE REACTION DIFFUSION EQUATIONS

Sun Zhizhong Li Xueling Department of Mathematics, Southeast University, Nanjing 210096, China  
The article is devoted to a compact alternate direct implicit difference method for the two-dimensinonal constant coefficient reaction-diffusion equations. Firstly, a compact difference scheme is derived by the combinatioin of the method of reduction of order and the method of reduction of dimension. The expression of the truncation error is given in detail. Secondly, a compact ADI difference scheme is presented by introducing a variable of intermediate value. Thirdly, a priori estimate of the solution of the compact ADI difference scheme in a discrete H1 norm is proved by the energy analysis method, with which the solvability and stability and convergence are achieved. The convergence order is O(τ2 +h4) in a discrete H1 norm. Fourthly, Richardson's extrapolation method is successfully applied to the compact ADI difference scheme and the approximate solution with accuracy O(τ4 +h6) is gained with once extrapolation. Finally, a numerical example demonstrates the theoretical results.
【Fund】: 东南大学科研基金(项目号:XJ0307113) 国家自然科学基金(项目号:10471023)资助项目.
【CateGory Index】: O241
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