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 34 articles , 1 standard article )

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  1. Corwin, Ivan Z.; Deift, Percy A.; Its, Alexander R.: Harold Widom’s work in random matrix theory (2022)
  2. Beck, Thomas; Bors, Isabel; Conte, Grace; Cox, Graham; Marzuola, Jeremy L.: Limiting eigenfunctions of Sturm-Liouville operators subject to a spectral flow (2021)
  3. Gutleb, Timon S.: A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels (2021)
  4. Jackaman, James; Pryer, Tristan: Conservative Galerkin methods for dispersive Hamiltonian problems (2021)
  5. Gutleb, Timon S.; Olver, Sheehan: A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle (2020)
  6. Gilles, Marc Aurèle; Townsend, Alex: Continuous analogues of Krylov subspace methods for differential operators (2019)
  7. Toppaladoddi, S.; Wettlaufer, John S.: The combined effects of shear and buoyancy on phase boundary stability (2019)
  8. Aiton, Kevin W.; Driscoll, Tobin A.: An adaptive partition of unity method for Chebyshev polynomial interpolation (2018)
  9. Klein, Christian; Stoilov, Nikola: Numerical approach to Painlevé transcendents on unbounded domains (2018)
  10. Almagro, Antonio; García-Villalba, Manuel; Flores, Oscar: A numerical study of a variable-density low-speed turbulent mixing layer (2017)
  11. Aurentz, Jared L.; Trefethen, Lloyd N.: Chopping a Chebyshev series (2017)
  12. Benoit, Alexandre; Joldeş, Mioara; Mezzarobba, Marc: Rigorous uniform approximation of D-finite functions using Chebyshev expansions (2017)
  13. Mireles James, J. D.; Murray, Maxime: Chebyshev-Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications (2017)
  14. Doc, Jean-Baptiste; Lihoreau, Bertrand; Félix, Simon; Pagneux, Vincent: Bremmer series for the multimodal sound propagation in inhomogeneous waveguides (2016)
  15. 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)
  16. Montanelli, Hadrien; Gushterov, Nikola I.: Computing planar and spherical choreographies (2016)
  17. Grava, Tamara; Kapaev, Andrei; Klein, Christian: On the tritronquée solutions of (\mathrmP_\mathrmI^2) (2015)
  18. Townsend, Alex; Olver, Sheehan: The automatic solution of partial differential equations using a global spectral method (2015)
  19. 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)
  20. Jarlebring, Elias; Güttel, Stefan: A spatially adaptive iterative method for a class of nonlinear operator eigenproblems (2014)

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