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Analysis and applications of the exponential time differencing schemes and their contour integration modifications. (English) Zbl 1080.65074
Authors’ abstract: We study 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.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
Software:
RODAS
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