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 185 articles )

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  1. 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)
  2. Ghorbani, Asghar; Gachpazan, Morteza: A spectral quasilinearization parametric method for nonlinear two-point boundary value problems (2019)
  3. Nakashima, Satoshi; Luhar, Mitul; Fukagata, Koji: Reconsideration of spanwise rotating turbulent channel flows via resolvent analysis (2019)
  4. Patne, Ramkarn; Shankar, V.: Stability of flow through deformable channels and tubes: implications of consistent formulation (2019)
  5. 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)
  6. Daliri Birjandi, Mohammad Hossein; Saberi-Nadjafi, Jafar; Ghorbani, Asghar: A novel method for solving nonlinear Volterra integro-differential equation systems (2018)
  7. Elgindy, Kareem T.: Optimization via Chebyshev polynomials (2018)
  8. Gheorghiu, Călin-Ioan: On the numerical treatment of the eigenparameter dependent boundary conditions (2018)
  9. Gheorghiu, Călin-Ioan: Spectral collocation solutions to problems on unbounded domains (2018)
  10. Kelly, Helena L.; Mathias, Simon A.: Capillary processes increase salt precipitation during CO(_2) injection in saline formations (2018)
  11. Klein, Christian; Stoilov, Nikola: Numerical approach to Painlevé transcendents on unbounded domains (2018)
  12. 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)
  13. Oehler, Stephan Friedrich; Illingworth, Simon J.: Sensor and actuator placement trade-offs for a linear model of spatially developing flows (2018)
  14. Tang, Xiaojun; Shi, Yang; Xu, Heyong: Well conditioned pseudospectral schemes with tunable basis for fractional delay differential equations (2018)
  15. Alboussière, Thierry; Ricard, Yanick: Rayleigh-Bénard stability and the validity of quasi-Boussinesq or quasi-anelastic liquid approximations (2017)
  16. Auton, L. C.; MacMinn, C. W.: From arteries to boreholes: steady-state response of a poroelastic cylinder to fluid injection (2017)
  17. Boiko, Andrey V.; Demyanko, Kirill V.; Nechepurenko, Yuri M.: On computing the location of laminar-turbulent transition in compressible boundary layers (2017)
  18. Chen, Kevin K.; Spedding, Geoffrey R.: Boussinesq global modes and stability sensitivity, with applications to stratified wakes (2017)
  19. Fasondini, Marco; Fornberg, Bengt; Weideman, J. A. C.: Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces (2017)
  20. Foroozandeh, Zahra; Shamsi, Mostafa; Azhmyakov, Vadim; Shafiee, Masoud: A modified pseudospectral method for solving trajectory optimization problems with singular arc (2017)

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