期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 234, 期 2, 页码 317-342出版社
ELSEVIER
DOI: 10.1016/j.cam.2009.12.029
关键词
Spectral collocation; Fast methods; Time stepping
资金
- MULTIMAT Marie Curie Research Training Network [MRTN-CT-2004-505226]
In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit-explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral space preconditioned Chebyshev tau, real space Chebyshev integration and spectral space Chebyshev integration methods are compared in the L-2 and W-2.2 norms when solving linear fourth order boundary value problems; and in the L-infinity([0, T]; L-2) and L-infinity([0, T]; W-2.2) norms when solving initial boundary value problems. We find that the best Chebyshev method to use for high resolution computations of solutions to initial boundary value problems is the spectral space Chebyshev integration method which uses sparse matrix operations and has a computational cost comparable to Fourier spectral discretization. (C) 2009 Elsevier B.V. All rights reserved.
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