The chebop system for automatic solution of differential equations
Tobin A. Driscoll Folkmar Bornemann Lloyd N. Trefethen Email author Article

First Online: 22 November 2008 Received: 18 June 2008 Accepted: 21 September 2008 DOI :
10.1007/s10543-008-0198-4

Cite this article as: Driscoll, T., Bornemann, F. & Trefethen, L. Bit Numer Math (2008) 48: 701. doi:10.1007/s10543-008-0198-4
Abstract 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.

Key words chebfun chebop spectral method Chebyshev points object-oriented Matlab differential equations AMS subject classification (2000) 65L10, 65M70, 65N35

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Authors and Affiliations Tobin A. Driscoll Folkmar Bornemann Lloyd N. Trefethen Email author 1. Department of Mathematical Sciences University of Delaware Newark USA 2. Zentrum Mathematik – M3 Technical University of Munich Garching bei München Germany 3. Computing Laboratory University of Oxford Oxford UK