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% 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.
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