chebop

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 28 articles , 1 standard article )

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  1. Gilles, Marc Aurèle; Townsend, Alex: Continuous analogues of Krylov subspace methods for differential operators (2019)
  2. Toppaladoddi, S.; Wettlaufer, John S.: The combined effects of shear and buoyancy on phase boundary stability (2019)
  3. Aiton, Kevin W.; Driscoll, Tobin A.: An adaptive partition of unity method for Chebyshev polynomial interpolation (2018)
  4. Klein, Christian; Stoilov, Nikola: Numerical approach to Painlevé transcendents on unbounded domains (2018)
  5. Almagro, Antonio; García-Villalba, Manuel; Flores, Oscar: A numerical study of a variable-density low-speed turbulent mixing layer (2017)
  6. Aurentz, Jared L.; Trefethen, Lloyd N.: Chopping a Chebyshev series (2017)
  7. Benoit, Alexandre; Joldeş, Mioara; Mezzarobba, Marc: Rigorous uniform approximation of D-finite functions using Chebyshev expansions (2017)
  8. Mireles James, J. D.; Murray, Maxime: Chebyshev-Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications (2017)
  9. 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)
  10. Montanelli, Hadrien; Gushterov, Nikola I.: Computing planar and spherical choreographies (2016)
  11. Grava, Tamara; Kapaev, Andrei; Klein, Christian: On the tritronquée solutions of (\mathrmP_\mathrmI^2) (2015)
  12. Townsend, Alex; Olver, Sheehan: The automatic solution of partial differential equations using a global spectral method (2015)
  13. 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)
  14. Jarlebring, Elias; Güttel, Stefan: A spatially adaptive iterative method for a class of nonlinear operator eigenproblems (2014)
  15. Trimbitas, Radu; Grosan, Teodor; Pop, Ioan: Mixed convection boundary layer flow along vertical thin needles in nanofluids (2014)
  16. Wang, Li-Lian; Samson, Michael Daniel; Zhao, Xiaodan: A well-conditioned collocation method using a pseudospectral integration matrix (2014)
  17. Elgindy, K. T.; Smith-Miles, Kate A.: Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices (2013)
  18. Olver, Sheehan; Townsend, Alex: A fast and well-conditioned spectral method (2013)
  19. Birkisson, Asgeir; Driscoll, Tobin A.: Automatic Fréchet differentiation for the numerical solution of boundary-value problems (2012)
  20. Grava, T.; Klein, C.: A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions (2012)

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