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Geometric Integration
- Title
- Geometric Integration
- Funding
- ARC | Discovery Projects
- Contract (GA) number
- DP0559083
- Start Date
- 2005/01/01
- End Date
- 2007/12/31
- Open Access mandate
- no
- Organizations
- -
- More information
- http://purl.org/au-research/grants/arc/DP0559083
-
Computing stability of multi-dimensional travelling waves
Ledoux, Veerle; Malham, Simon J. A.; Niesen, Jitse; Thümmler, Vera (2008)
Projects: ARC | Geometric Integration (DP0559083)We present a numerical method for computing the pure-point spectrum associated with the linear stability of multi-dimensional travelling fronts to parabolic nonlinear systems. Our method is based on the Evans function shooting approach. Transverse to the direction of propagation we project the spectral equations onto a finite Fourier basis. This generates a large, linear, one-dimensional system of equations for the longitudinal Fourier coefficients. We construct the stable and unstable soluti...A Krylov subspace algorithm for evaluating the phi-functions appearing in exponential integrators
We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector representing the initial condition. The matrix function is a linear combination of the matrix exponential and other functions related to the exponential (the so-called phi-functions). Such computations are the major computational burden in the implementation of ... -
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