BIT Numerical Mathematics

, Volume 48, Issue 4, pp 701–723

The chebop system for automatic solution of differential equations

  • Tobin A. Driscoll
  • Folkmar Bornemann
  • Lloyd N. Trefethen
Article

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

chebfunchebopspectral methodChebyshev pointsobject-oriented Matlabdifferential equations

Copyright information

© Springer Science + Business Media B.V. 2008

Authors and Affiliations

  • Tobin A. Driscoll
    • 1
  • Folkmar Bornemann
    • 2
  • Lloyd N. Trefethen
    • 3
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  2. 2.Zentrum Mathematik – M3Technical University of MunichGarching bei MünchenGermany
  3. 3.Computing LaboratoryUniversity of OxfordOxfordUK