期刊
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
卷 26, 期 1, 页码 37-60出版社
JOHN WILEY & SONS INC
DOI: 10.1002/num.20414
关键词
ADI scheme; asymptotic expansion; compact ADI scheme; discrete energy method; parabolic equation; Richardson extrapolation
资金
- National Natural Science Foundation of China [10871044]
Alternating direction implicit (ADI) schemes are compuationally efficient and widely utilized for numerical approximation of the multidimensional parabolic equations. By using the discrete energy method, it is shown that the ADI solution is unconditionally convergent with the convergence order of two in the maximum. Considering all asymptotic expansion of the difference Solution, we obtain a fourth-order, in both time and space, approximation by one Richardson extrapolation. Extension of our technique to the higher-order compact ADI schemes also yields the maximum norm error estimate of the discrete solution. And by one extrapolation, we obtain a sixth order accurate approximation when the time step is proportional to the squares of the spatial size. An numerical example is presented to Support our theoretical results. (C) 2008 Wiley Periodicals, Inc. Number Methods Partial Differential Eq 26: 37-60, 2010
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