% Matlab Differentiation Matrix Suite%%by J.A.C. Weideman and S.C. Reddy%%This is a software package consisting of seventeen {\sc Matlab}%functions for solving differential equations on bounded, periodic,%and infinite intervals by the spectral collocation (pseudospectral)%method.  The package includes functions for generating differentiation%matrices of arbitrary order corresponding to Chebyshev, Hermite,%Laguerre, Fourier, and sinc interpolants. In addition, functions%are included for computing derivatives via the fast Fourier transform%for Chebyshev, Fourier, and Sinc interpolants.  Auxiliary functions%are included for incorporating boundary conditions, performing%interpolation using barycentric formulas, and computing roots of%orthogonal polynomials.  In the accompanying paper it is demonstrated%how to use the package by solving eigenvalue, boundary value, and%initial value problems arising in the fields of special functions,%quantum mechanics, nonlinear waves, and hydrodynamic stability.%(Paper located at http://ucs.orst.edu/~weidemaj/differ.html) %%%   ------------------------------------------------------------%   |  We have made every effort to test these functions.      |%   |  However, NO GUARANTEES are made about their validity.   |%   |  Please send a email to weideman@math.orst.edu or        |%   |  reddy@math.orst.edu if you find bugs or have comments   |%   ------------------------------------------------------------%%Summary of the {\sc Matlab} functions in the suite:%--------------------------------------------------%%I. Differentiation Matrices (Polynomial Based)%%1.    poldif.m: General differentiation matrices.%2.   chebdif.m: Chebyshev differentiation matrices. %3.    herdif.m: Hermite differentiation matrices. %4.    lagdif.m: Laguerre differentiation matrices.%%II. Differentiation Matrices (Non-Polynomial)%%1.   fourdif.m: Fourier differentiation matrices.  %2.   sincdif.m: Sinc differentiation matrices. %%III. Boundary Conditions%%1.   cheb2bc.m: Chebyshev 2nd derivative matrix%                incorporating Robin conditions.%2.    cheb4c.m: Chebyshev 4th derivative matrix%                incorporating clamped conditions.%%IV. Interpolation%%1.    polint.m: Barycentric polynomial interpolation on%                arbitrary distinct nodes%2.   chebint.m: Barycentric polynomial interpolation on%                Chebyshev nodes. %3.   fourint.m: Barycentric trigonometric interpolation at%                equidistant nodes. %%V. Transform-based derivatives  %%1. chebdifft.m: Chebyshev derivative%2. fourdifft.m: Fourier derivative%3.  sincdift.m: Sinc derivative %%VI. Roots of Orthogonal Polynomials%%1.  legroots.m: Roots of Legendre polynomials.%2.  lagroots.m: Roots of Laguerre polynomials. %3.  herroots.m: Roots of Hermite polynomials.  %%VII. Examples%%1.     cerfa.m: Function file for computing the complementary %                error function.  Boundary condition (a) is used.%2.     cerfb.m: Same as cerfa.m but boundary condition (b) is used.%3.   matplot.m: Script file for plotting the characteristic curves %                of Mathieu's equation.%4.       ce0.m: Function file for computing the Mathieu cosine%                elliptic function.%5.     sineg.m: Script file for solving the sine-Gordon equation.%6.     sgrhs.m: Function file for computing the right-hand side of %                the sine-Gordon system.%7.    schrod.m: Script file for computing the eigenvalues of the %                Schr\"odinger equation.%8.    orrsom.m: Script file for computing the eigenvalues of the %                Orr-Sommerfeld equation.