Differentiation Matrix Suite

A Matlab differentiation matrix suite. A software suite consisting of 17 MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral) method is presented. It includes functions for computing derivatives of arbitrary order corresponding to Chebyshev, Hermite, Laguerre, Fourier, and sinc interpolants. Auxiliary functions are included for incorporating boundary conditions, performing interpolation using barycentric formulas, and computing roots of orthogonal polynomials. It is demonstrated how to use the package for solving eigenvalue, boundary value, and initial value problems arising in the fields of special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 145 articles )

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  1. de la Hoz, Francisco; Vadillo, Fernando: Numerical simulations of time-dependent partial differential equations (2016)
  2. Du, Kui: On well-conditioned spectral collocation and spectral methods by the integral reformulation (2016)
  3. Heins, Peter H.; Jones, Bryn Ll.; Sharma, Ati S.: Passivity-based output-feedback control of turbulent channel flow (2016)
  4. Janečka, A.; Průša, V.; Rajagopal, K.R.: Euler-Bernoulli type beam theory for elastic bodies with nonlinear response in the small strain range (2016)
  5. Xu, Kuan: The Chebyshev points of the first kind (2016)
  6. An, Jing; Luo, Zhendong; Li, Hong; Sun, Ping: Reduced-order extrapolation spectral-finite difference scheme based on POD method and error estimation for three-dimensional parabolic equation (2015)
  7. Black, J.P.; Breward, C.J.W.; Howell, P.D.: Two-dimensional modeling of electron flow through a poorly conducting layer (2015)
  8. Esmaeili, Shahrokh; Garrappa, Roberto: A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation (2015)
  9. Gheorghiu, Călin-Ioan: Pseudospectral solutions to some singular nonlinear BVPs (2015)
  10. Hale, Nicholas; Weideman, J.A.C.: Contour integral solution of elliptic PDEs in cylindrical domains (2015)
  11. Jääskeläinen, Markku: The wave function as matter density: ontological assumptions and experimental consequences (2015)
  12. Ngounda, Edgard; Patidar, Kailash C.: A Laplace transform approach for pricing European options (2015)
  13. Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.: Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems (2015)
  14. Boiko, Andrey V.; Nechepurenko, Yuri M.; Abalakin, Ilya V.; Bobkov, Vladimir G.: Numerical prediction of laminar-turbulent transition on an airfoil (2014)
  15. Boyd, John P.: Solving transcendental equations. The Chebyshev polynomial proxy and other numerical rootfinders, perturbation series, and oracles (2014)
  16. Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin: Fourier spectral methods for fractional-in-space reaction-diffusion equations (2014)
  17. Lessard, Jean-Philippe; Reinhardt, Christian: Rigorous numerics for nonlinear differential equations using Chebyshev series (2014)
  18. Liu, Wenjie; Wu, Boying; Sun, Jiebao: Some numerical algorithms for solving the highly oscillatory second-order initial value problems (2014)
  19. Motsa, Sandile S.: On the practical use of the spectral homotopy analysis method and local linearisation method for unsteady boundary-layer flows caused by an impulsively stretching plate (2014)
  20. Sadiq, Burhan; Viswanath, Divakar: Finite difference weights, spectral differentiation, and superconvergence (2014)

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