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 211 articles )

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  1. Amiraslani, Amirhossein; Corless, Robert M.; Gunasingam, Madhusoodan: Differentiation matrices for univariate polynomials (2020)
  2. Baingne, Mahendra; Sharma, Gaurav: Effect of wall deformability on the stability of shear-imposed film flow past an inclined plane (2020)
  3. Crespo, S.; Fasondini, M.; Klein, C.; Stoilov, N.; Vallée, C.: Multidomain spectral method for the Gauss hypergeometric function (2020)
  4. Hwang, Yongyun; Eckhardt, Bruno: Attached eddy model revisited using a minimal quasi-linear approximation (2020)
  5. Liu, Chang; Gayme, Dennice F.: An input-output based analysis of convective velocity in turbulent channels (2020)
  6. Wong, Clint Y. H.; Trinh, Philippe H.; Chapman, S. Jonathan: Shear-induced instabilities of flows through submerged vegetation (2020)
  7. 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)
  8. 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)
  9. Dawson, Scott T. M.; McKeon, Beverley J.: On the shape of resolvent modes in wall-bounded turbulence (2019)
  10. Demyanko, Kirill V.: Numerical model for the investigation of hydrodynamic stability of shear flows in pipes of elliptic cross-section (2019)
  11. 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)
  12. 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)
  13. Ghorbani, Asghar; Gachpazan, Morteza: A spectral quasilinearization parametric method for nonlinear two-point boundary value problems (2019)
  14. Ghorbani, Asghar; Tavakoli, Mostafa: An adaptive spectral parametric method for solving nonlinear initial value problems (2019)
  15. Nakashima, Satoshi; Luhar, Mitul; Fukagata, Koji: Reconsideration of spanwise rotating turbulent channel flows via resolvent analysis (2019)
  16. Patne, Ramkarn; Shankar, V.: Stability of flow through deformable channels and tubes: implications of consistent formulation (2019)
  17. Taher, Anis Haytham Saleh: Computing high-index eigenvalues of singular Sturm-Liouville problems (2019)
  18. Zhuang, Meiling; Miao, Changqing; Wan, Caihong: A highly accurate collocation method for linear and nonlinear vibration problems of multi-degree-of-freedom systems based on barycentric interpolation (2019)
  19. 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)
  20. Daliri Birjandi, Mohammad Hossein; Saberi-Nadjafi, Jafar; Ghorbani, Asghar: A novel method for solving nonlinear Volterra integro-differential equation systems (2018)

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