Journal
BIT NUMERICAL MATHEMATICS
Volume 45, Issue 2, Pages 307-328Publisher
SPRINGER
DOI: 10.1007/s10543-005-7141-8
Keywords
time integration schemes; exponential time differencing; contour integrals; Fourier spectral methods; stability; Fourier analysis; energy estimates; maximum principle; Allen-Cahn equations; phase transitions
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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.
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