Analysis and applications of the exponential time differencing schemes and their contour integration modifications

被引：99
|
作者：
Du, Q [1 ]
Zhu, WX [1 ]
机构：
[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA
来源：
BIT NUMERICAL MATHEMATICS | 2005年 / 45卷 / 02期
关键词：
time integration schemes; exponential time differencing; contour integrals; Fourier spectral methods; stability; Fourier analysis; energy estimates; maximum principle; Allen-Cahn equations; phase transitions;
D O I：
10.1007/s10543-005-7141-8
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We study in this paper the exponential time differencing (ETD) schemes and their modifications via complex contour integrations for the numerical solutions of parabolic type equations. We illustrate that the contour integration shares an added advantage of improving the stability of the time integration. In addition, we demonstrate the effectiveness of the ETD type schemes through the numerical solution of a typical problem in phase field modeling and through the comparisons with other existing methods.
引用
收藏
页码：307 / 328
页数：22
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