Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 26, Issue 4, Pages 1214-1233Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S1064827502410633
Keywords
ETD; exponential time-differencing; KdV; Kuramoto-Sivashinsky-Burgers; Allen-Cahn; implicit-explicit; split step; integrating factor
Categories
Ask authors/readers for more resources
A modification of the exponential time-differencing fourth-order Runge-Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators. A comparison is made of the performance of this modified exponential time-differencing (ETD) scheme against the competing methods of implicit-explicit differencing, integrating factors, time-splitting, and Fornberg and Driscoll's sliders for the KdV, Kuramoto-Sivashinsky, Burgers, and Allen-Cahn equations in one space dimension. Implementation of the method is illustrated by short MATLAB programs for two of the equations. It is found that for these applications with fixed time steps, the modified ETD scheme is the best.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available