The Mathematical Institute, University of Oxford, Eprints Archive

Fourth-order time stepping for stiff PDEs

Kassam, Aly-Khan and Trefethen, Lloyd N. (2003) Fourth-order time stepping for stiff PDEs. Technical Report. Unspecified. (Submitted)

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Abstract

A modification of the ETDRK4 (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 non-diagonal operators. A comparison is made of the performance of this modified 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.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1194
Deposited By:Lotti Ekert
Deposited On:18 May 2011 08:12
Last Modified:18 May 2011 08:12

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