@Article{AAMM-9-2,
author = {Chuanmiao, Chen and Xiangqi, Wang and Hu, Hongling},
title = {A High-Efficient Algorithm for Parabolic Problems with Time-Dependent Coefficients},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {2},
pages = {501--514},
abstract = {<p style="text-align: justify;">A high-efficient algorithm to solve Crank-Nicolson scheme for variable coefficient parabolic problems is studied in this paper, which consists of the Function Time-Extrapolation
Algorithm (FTEA) and Matrix Time-Extrapolation Algorithm (MTEA).
First, FTEA takes a linear combination of previous $l$ level solutions ($U^{n,0}$=$∑^l_{i=1}$$a_i$$U^{n−i}$)
as good initial value of $U^n$ (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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2015.m1281},
url = {https://global-sci.com/article/73263/a-high-efficient-algorithm-for-parabolic-problems-with-time-dependent-coefficients}
}