The chebop system for automatic solution of differential equations. In Matlab, it would be good to be able to solve a linear differential equation by typing u=L , 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.

References in zbMATH (referenced in 17 articles , 1 standard article )

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  1. Essaghir, Elhoucine; Haddout, Youssef; Oubarra, Abdelaziz; Lahjomri, Jawad: Non-similar solution of the forced convection of laminar gaseous slip flow over a flat plate with viscous dissipation: linear stability analysis for local similar solution (2016)
  2. Montanelli, Hadrien; Gushterov, Nikola I.: Computing planar and spherical choreographies (2016)
  3. Grava, Tamara; Kapaev, Andrei; Klein, Christian: On the tritronquée solutions of $\mathrmP_\mathrmI^2$ (2015)
  4. Foster, J.M.; Snaith, H.J.; Leijtens, T.; Richardson, G.: A model for the operation of perovskite based hybrid solar cells: formulation, analysis, and comparison to experiment (2014)
  5. Jarlebring, Elias; Güttel, Stefan: A spatially adaptive iterative method for a class of nonlinear operator eigenproblems (2014)
  6. Wang, Li-Lian; Samson, Michael Daniel; Zhao, Xiaodan: A well-conditioned collocation method using a pseudospectral integration matrix (2014)
  7. Elgindy, K.T.; Smith-Miles, Kate A.: Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices (2013)
  8. Olver, Sheehan; Townsend, Alex: A fast and well-conditioned spectral method (2013)
  9. Grava, T.; Klein, C.: A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions (2012)
  10. Collins, Pieter; Niqui, Milad; Revol, Nathalie: A validated real function calculus (2011)
  11. Olver, Sheehan: Numerical solution of Riemann-Hilbert problems: Painlevé II (2011)
  12. Bornemann, F.: On the numerical evaluation of distributions in random matrix theory: a review (2010)
  13. Bornemann, Folkmar: On the numerical evaluation of Fredholm determinants (2010)
  14. Driscoll, Tobin A.: Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations (2010)
  15. Platte, R.B.; Trefethen, L.N.: Chebfun: A new kind of numerical computing (2010)
  16. Zhang, Xuecang: Mapped barycentric Chebyshev differentiation matrix method for the solution of regular Sturm-Liouville problems (2010)
  17. Driscoll, Tobin A.; Bornemann, Folkmar; Trefethen, Lloyd N.: The chebop system for automatic solution of differential equations (2008)