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 219 articles )

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  1. Amiraslani, Amirhossein; Corless, Robert M.; Gunasingam, Madhusoodan: Differentiation matrices for univariate polynomials (2020)
  2. Andò, Alessia; Breda, Dimitri: Collocation techniques for structured populations modeled by delay equations (2020)
  3. Baingne, Mahendra; Sharma, Gaurav: Effect of wall deformability on the stability of shear-imposed film flow past an inclined plane (2020)
  4. Crespo, S.; Fasondini, M.; Klein, C.; Stoilov, N.; Vallée, C.: Multidomain spectral method for the Gauss hypergeometric function (2020)
  5. Fung, Lloyd; Bearon, Rachel N.; Hwang, Yongyun: Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe (2020)
  6. Hwang, Yongyun; Eckhardt, Bruno: Attached eddy model revisited using a minimal quasi-linear approximation (2020)
  7. Kaoullas, G.; Johnson, E. R.: Trapped continental shelf waves with a free surface (2020)
  8. Liu, Chang; Gayme, Dennice F.: An input-output based analysis of convective velocity in turbulent channels (2020)
  9. Martini, Eduardo; Cavalieri, André V. G.; Jordan, Peter; Towne, Aaron; Lesshafft, Lutz: Resolvent-based optimal estimation of transitional and turbulent flows (2020)
  10. Moutsinga, Claude Rodrigue Bambe; Pindza, Edson; Maré, Eben: A time multidomain spectral method for valuing affine stochastic volatility and jump diffusion models (2020)
  11. Önder, Asim; Liu, Philip L.-F.: Stability of the solitary wave boundary layer subject to finite-amplitude disturbances (2020)
  12. Wong, Clint Y. H.; Trinh, Philippe H.; Chapman, S. Jonathan: Shear-induced instabilities of flows through submerged vegetation (2020)
  13. Abid, M.; Kharif, C.; Hsu, H.-C.; Chen, Y.-Y.: Transverse instability of gravity-capillary solitary waves on deep water in the presence of constant vorticity (2019)
  14. Boiko, Andrey V.; Demyanko, Kirill V.; Nechepurenko, Yuri M.: Asymptotic boundary conditions for the analysis of hydrodynamic stability of flows in regions with open boundaries (2019)
  15. Dawson, Scott T. M.; McKeon, Beverley J.: On the shape of resolvent modes in wall-bounded turbulence (2019)
  16. Demyanko, Kirill V.: Numerical model for the investigation of hydrodynamic stability of shear flows in pipes of elliptic cross-section (2019)
  17. Dutta, Satarupa; Ghosh, Abir; Pattader, Partho Sarathi Gooh; Bandyopadhyay, Dipankar: Electric field mediated von Kármán vortices in stratified microflows: transition from linear instabilities to coherent mixing (2019)
  18. Foroozandeh, Z.; Shamsi, M.; de Pinho, M. d. R.: A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems (2019)
  19. Ghorbani, Asghar; Gachpazan, Morteza: A spectral quasilinearization parametric method for nonlinear two-point boundary value problems (2019)
  20. Ghorbani, Asghar; Tavakoli, Mostafa: An adaptive spectral parametric method for solving nonlinear initial value problems (2019)

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