The chebop system for automatic solution of differential equations
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In Matlab, it would be good to be able to solve a linear differential equation by typing u = L\f, where f, u, and L are representations of the right-hand side, the solution, and the differential operator with boundary conditions. Similarly it would be good to be able to exponentiate an operator with expm(L) or determine eigenvalues and eigenfunctions with eigs(L). A system is described in which such calculations are indeed possible, at least in one space dimension, based on the previously developed chebfun system in object-oriented Matlab. The algorithms involved amount to spectral collocation methods on Chebyshev grids of automatically determined resolution.
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- The chebop system for automatic solution of differential equations
BIT Numerical Mathematics
Volume 48, Issue 4 , pp 701-723
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- Springer Netherlands
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- spectral method
- Chebyshev points
- object-oriented Matlab
- differential equations
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- Author Affiliations
- 1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA
- 2. Zentrum Mathematik – M3, Technical University of Munich, 85747, Garching bei München, Germany
- 3. Computing Laboratory, University of Oxford, Parks Rd., Oxford, OX1 3QD, UK