A high-efficient algorithm to solve Crank-Nicolson scheme for variable coef- ficient parabolic problems is studied in this paper, which consists of the Function TimeExtrapolation Algorithm (FTEA) and Matrix Time-Extrapolation Algorithm (MTEA). First, FTEA takes a linear combination of previous l level solutions (Un,0=∑ l i=1 aiUn−i ) as good initial value of Un (see Time-extrapolation algorithm (TEA) for linear parabolic problems, J. Comput. Math., 32(2) (2014), pp. 183–194), so that Conjugate Gradient (CG)-iteration counts decrease to 1/3∼1/4 of direct CG. Second, MTEA uses a linear combination of exact matrix values in level L, L+s, L+2s to predict matrix values in the following s−1 levels, and the coefficients of the linear combination is deduced by the quadric interpolation formula, then fully recalculate the matrix values at time level L+3s, and continue like this iteratively. Therefore, the number of computing the full matrix decreases by a factor 1/s. Last, the MTEA is analyzed in detail and the effectiveness of new method is verified by numerical experiments.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1281}, url = {http://global-sci.org/intro/article_detail/aamm/12161.html} }