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 169 articles )

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  1. Gheorghiu, Călin-Ioan: On the numerical treatment of the eigenparameter dependent boundary conditions (2018)
  2. Gheorghiu, Călin-Ioan: Spectral collocation solutions to problems on unbounded domains (2018)
  3. Alboussière, Thierry; Ricard, Yanick: Rayleigh-Bénard stability and the validity of quasi-Boussinesq or quasi-anelastic liquid approximations (2017)
  4. Boiko, Andrey V.; Demyanko, Kirill V.; Nechepurenko, Yuri M.: On computing the location of laminar-turbulent transition in compressible boundary layers (2017)
  5. Chen, Kevin K.; Spedding, Geoffrey R.: Boussinesq global modes and stability sensitivity, with applications to stratified wakes (2017)
  6. Fasondini, Marco; Fornberg, Bengt; Weideman, J.A.C.: Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces (2017)
  7. Foroozandeh, Zahra; Shamsi, Mostafa; Azhmyakov, Vadim; Shafiee, Masoud: A modified pseudospectral method for solving trajectory optimization problems with singular arc (2017)
  8. Li, Yiqun; Wu, Boying; Leok, Melvin: Spectral variational integrators for semi-discrete Hamiltonian wave equations (2017)
  9. Oshagh, M.Khaksar-E; Shamsi, M.: Direct pseudo-spectral method for optimal control of obstacle problem-an optimal control problem governed by elliptic variational inequality (2017)
  10. Tang, Xiaojun; Shi, Yang; Wang, Li-Lian: A new framework for solving fractional optimal control problems using fractional pseudospectral methods (2017)
  11. Tang, Xiaojun; Shi, Yang; Xu, Heyong: Fractional pseudospectral schemes with equivalence for fractional differential equations (2017)
  12. Tissot, Gilles; Zhang, Mengqi; Lajús, Francisco C.jun.; Cavalieri, André V.G.; Jordan, Peter: Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer (2017)
  13. Zare, Armin; Jovanović, Mihailo R.; Georgiou, Tryphon T.: Colour of turbulence (2017)
  14. de la Hoz, Francisco; Vadillo, Fernando: Numerical simulations of time-dependent partial differential equations (2016)
  15. Du, Kui: On well-conditioned spectral collocation and spectral methods by the integral reformulation (2016)
  16. Gheorghiu, Călin-Ioan: Spectral collocation solutions to systems of boundary layer type (2016)
  17. Heins, Peter H.; Jones, Bryn Ll.; Sharma, Ati S.: Passivity-based output-feedback control of turbulent channel flow (2016)
  18. Janečka, A.; Průša, V.; Rajagopal, K.R.: Euler-Bernoulli type beam theory for elastic bodies with nonlinear response in the small strain range (2016)
  19. Sabeh, Z.; Shamsi, M.; Dehghan, Mehdi: Distributed optimal control of the viscous Burgers equation via a Legendre pseudo-spectral approach (2016)
  20. Xu, Kuan: The Chebyshev points of the first kind (2016)

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