BIT Numerical Mathematics

, Volume 45, Issue 2, pp 307–328 | Cite as

Analysis and Applications of the Exponential Time Differencing Schemes and Their Contour Integration Modifications

  • Qiang Du
  • Wenxiang Zhu


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.

Key words

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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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUSA

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