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 249 articles )

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  1. Ding, Zhaodong; Mu, Kai; Si, Ting; Jian, Yongjun: Linear instability analysis of a viscoelastic jet in a co-flowing gas stream (2022)
  2. Klein, Christian; Stoilov, Nikola: Spectral approach to Korteweg-de Vries equations on the compactified real line (2022)
  3. Nawaz, A.; Samad, A.; Ullah, L.: On the steady laminar boundary-layer flow over the family of rotating tori (2022)
  4. Nogueira, Petrônio A. S.; Jaunet, Vincent; Mancinelli, Matteo; Jordan, Peter; Edgington-Mitchell, Daniel: Closure mechanism of the A1 and A2 modes in jet screech (2022)
  5. Abrahamsen, Dylan; Fornberg, Bengt: On the infinite order limit of Hermite-based finite difference schemes (2021)
  6. Chang, Yu-Jen; Chern, Ruey-Lin; Chou, Yi-Ju: Transient instability in long, tilted water columns with fast-settling, particle-laden layers (2021)
  7. Demyanko, K. V.: On using the shell theory in stability analysis of fluid flows in compliant pipes (2021)
  8. Dostalík, Mark; Matyska, Ctirad; Průša, Vít: Weakly nonlinear analysis of Rayleigh-Bénard convection problem in extended Boussinesq approximation (2021)
  9. He, Xuerao; Zhang, Mengqi: On the flow instability under thermal and electric fields: a linear analysis (2021)
  10. Khalid, Mohammad; Chaudhary, Indresh; Garg, Piyush; Shankar, V.; Subramanian, Ganesh: The centre-mode instability of viscoelastic plane Poiseuille flow (2021)
  11. Klein, Christian; Stoilov, Nikola: Numerical study of break-up in solutions to the dispersionless Kadomtsev-Petviashvili equation (2021)
  12. Liu, Chang; Gayme, Dennice F.: Structured input-output analysis of transitional wall-bounded flows (2021)
  13. Liu, Hongyan; Huang, Jin; Zhang, Wei: Numerical algorithm based on extended barycentric Lagrange interpolant for two dimensional integro-differential equations (2021)
  14. Li, Y.; Sam, C. N.; Hon, Y. C.; Ng, K. S.: An integration preconditioning method for solving option pricing problems (2021)
  15. Meyer, Marcela Molina; Prieto Medina, Frank Richard: Polar differentiation matrices for the Laplace equation in the disk under nonhomogeneous Dirichlet, Neumann and Robin boundary conditions and the biharmonic equation under nonhomogeneous Dirichlet conditions (2021)
  16. Nogueira, Petrônio A. S.; Edgington-Mitchell, Daniel M.: Investigation of supersonic twin-jet coupling using spatial linear stability analysis (2021)
  17. Park, Junho; Moon, Sungju; Seo, Jaemyeong Mango; Baik, Jong-Jin: Systematic comparison between the generalized Lorenz equations and DNS in the two-dimensional Rayleigh-Bénard convection (2021)
  18. Rauch, Reuben; Trummer, Manfred R.; Williams, J. F.: A spectral collocation method for mixed functional differential equations (2021)
  19. Saito, Takeshi; Yagasaki, Kazuyuki: Chebyshev spectral methods for computing center manifolds (2021)
  20. Scarabel, Francesca; Diekmann, Odo; Vermiglio, Rossana: Numerical bifurcation analysis of renewal equations via pseudospectral approximation (2021)

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