STABILITY ANALYSIS AND APPLICATION OF THE EXPONENTIAL TIME DIFFERENCING SCHEMES 1)

Exponential time dierencing schemes are time integration methods that can be eciently combined with spatial spectral approximations to provide very high resolution to the smooth solutions of some linear and nonlinear partial dieren tial equations. We study in this paper the stability properties of some exponential time dierencing schemes. We also present their application to the numerical solution of the scalar Allen-Cahn equation in two and three dimensional spaces.

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