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 200 articles )

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  1. 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)
  2. 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)
  3. Dawson, Scott T. M.; McKeon, Beverley J.: On the shape of resolvent modes in wall-bounded turbulence (2019)
  4. 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)
  5. 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)
  6. Ghorbani, Asghar; Gachpazan, Morteza: A spectral quasilinearization parametric method for nonlinear two-point boundary value problems (2019)
  7. Ghorbani, Asghar; Tavakoli, Mostafa: An adaptive spectral parametric method for solving nonlinear initial value problems (2019)
  8. Mandel, Tracy L.; Gakhar, Saksham; Chung, Hayoon; Rosenzweig, Itay; Koseff, Jeffrey R.: On the surface expression of a canopy-generated shear instability (2019)
  9. Nakashima, Satoshi; Luhar, Mitul; Fukagata, Koji: Reconsideration of spanwise rotating turbulent channel flows via resolvent analysis (2019)
  10. Patne, Ramkarn; Shankar, V.: Stability of flow through deformable channels and tubes: implications of consistent formulation (2019)
  11. Taher, Anis Haytham Saleh: Computing high-index eigenvalues of singular Sturm-Liouville problems (2019)
  12. Boiko, A. V.; Demyanko, K. V.; Nechepurenko, Yu. M.: Numerical analysis of spatial hydrodynamic stability of shear flows in ducts of constant cross section (2018)
  13. Daliri Birjandi, Mohammad Hossein; Saberi-Nadjafi, Jafar; Ghorbani, Asghar: A novel method for solving nonlinear Volterra integro-differential equation systems (2018)
  14. Elgindy, Kareem T.: Optimization via Chebyshev polynomials (2018)
  15. Gheorghiu, Călin-Ioan: Spectral collocation solutions to problems on unbounded domains (2018)
  16. Gheorghiu, Călin-Ioan: On the numerical treatment of the eigenparameter dependent boundary conditions (2018)
  17. Kelly, Helena L.; Mathias, Simon A.: Capillary processes increase salt precipitation during CO(_2) injection in saline formations (2018)
  18. Klein, Christian; Stoilov, Nikola: Numerical approach to Painlevé transcendents on unbounded domains (2018)
  19. Labrosse, Stéphane; Morison, Adrien; Deguen, Renaud; Alboussière, Thierry: Rayleigh-Bénard convection in a creeping solid with melting and freezing at either or both its horizontal boundaries (2018)
  20. Mondal, Kartick; Ghosh, Abir; Chaudhuri, Joydip; Bandyopadhyay, Dipankar: Electric-field-mediated instability modes and fréedericksz transition of thin nematic films (2018)

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