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<HTML><HEAD> <TITLE>A Matlab Differentiation Matrix Suite</TITLE></HEAD><BODY BGCOLOR="#FFFFFF"><P><H2>A Matlab Differentiation Matrix Suite</H2><P><P>This is a software suite designed for MATLAB 5 consistingof seventeen functions for solving differential equations by the spectral collocation (a.k.a. pseudospectral) method. It includes functions for computing differentiation matrices of arbitrary order corresponding to Chebyshev, Hermite, Laguerre, Fourier, and sinc interpolants. It also includes FFT-based routines for Fourier,Chebyshev and sinc differentiation. Auxiliary functions are included for incorporating boundary conditions, performing interpolation using barycentric formulas, and computing roots of orthogonal polynomials. <P>In the accompanying paper 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.<P><H3>Paper</H3><P>Download the <A HREF="paper.ps.gz" tppabs="http://ucs.orst.edu/~weidemaj/differ/paper.ps.gz">compressed version</A> of the paper (paper.ps.gz, gzipped PostScript 0.4MB), orthe <A HREF="paper.ps" tppabs="http://ucs.orst.edu/~weidemaj/differ/paper.ps">uncompressed version </A> (paper.ps, PostScript 1.2MB).<P><H3>Functions</H3><P>We have made every effort to test these functions. However, NO GUARANTEESare made about their validity. Please contact us at<A HREF="mailto:weideman@math.orst.edu">weideman@math.orst.edu</A> or<A HREF="mailto:reddy@math.orst.edu">reddy@math.orst.edu</A>if you find bugs or have comments!<P>The entire set of functions is available in a <A HREF="dmsuite.tar" tppabs="http://ucs.orst.edu/~weidemaj/differ/dmsuite.tar">tar file</A>. To process, issue the command<P>tar -xvf dmsuite.tar<P>For a .zip version, please go to this MathWorks<A HREF="javascript:if(confirm('http://www.mathworks.com/support/ftp/diffeqv5.shtml \n\nThis file was not retrieved by Teleport Pro, because it is addressed on a domain or path outside the boundaries set for its Starting Address. \n\nDo you want to open it from the server?'))window.location='http://www.mathworks.com/support/ftp/diffeqv5.shtml'" tppabs="http://www.mathworks.com/support/ftp/diffeqv5.shtml">site.</A><P>Individual files can also be downloaded as text files:<H4>Table of Contents<BR></H4><UL><LI><A HREF="Contents.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/Contents.m">Contents.m</A> </UL><H4>Differentiation Matrices (Polynomial Based)<BR></H4><UL><LI><A HREF="poldif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/poldif.m">poldif.m</A> (General differentiation matrices)<LI><A HREF="chebdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/chebdif.m">chebdif.m</A> (Chebshev differentiation matrices)<LI><A HREF="herdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/herdif.m">herdif.m</A> (Hermite differentiationmatrices)<BR>Requires: <A HREF="herroots.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/herroots.m">herroots.m</A>,<A HREF="poldif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/poldif.m">poldif.m</A><LI><A HREF="lagdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/lagdif.m">lagdif.m</A> (Laguerre differentiationmatrices)<BR>Requires: <A HREF="lagroots.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/lagroots.m">lagroots.m</A>,<A HREF="poldif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/poldif.m">poldif.m</A></UL><H4>Differentiation Matrices (Non-Polynomial)<BR></H4><UL><LI><A HREF="fourdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/fourdif.m">fourdif.m</A> (Fourier differentiation matrices)<LI><A HREF="sincdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/sincdif.m">sincdif.m</A> (Sinc differentiation matrices)</UL><H4>Boundary Conditions<BR></H4><UL><LI><A HREF="cheb2bc.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/cheb2bc.m">cheb2bc.m </A>(Chebyshev 2nd derivativematrix incorporating Robin boundary conditions)<BR> Requires:<A HREF="chebdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/chebdif.m">chebdif.m</A><LI><A HREF="cheb4c.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/cheb4c.m">cheb4c.m</A> (Chebyshev 4th derivative matrixincorporating clamped boundary conditions)</UL><H4>Interpolation<BR></H4><UL><LI><A HREF="polint.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/polint.m">polint.m</A> (Barycentric polynomialinterpolation on arbitrary distinct nodes)<LI><A HREF="chebint.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/chebint.m">chebint.m</A> (Barycentric polynomial interpolationon Chebyshev points)<LI><A HREF="fourint.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/fourint.m">fourint.m</A> (Barycentric trigonometric interpolationat equidistant nodes)</UL><H4>Transform-Based Derivatives<BR></H4><UL><LI><A HREF="chebdifft.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/chebdifft.m">chebdifft.m</A> (FFT-based Chebyshev derivative)<LI><A HREF="fourdifft.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/fourdifft.m">fourdifft.m</A> (FFT-based Fourier derivative)<LI><A HREF="sincdifft.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/sincdifft.m">sincdifft.m</A> (FFT-based sinc derivative)</UL><H4>Roots of Orthogonal Polynomials<BR></H4><UL><LI><A HREF="legroots.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/legroots.m">legroots.m </A>(Roots of Legendre polynomials)<LI><A HREF="lagroots.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/lagroots.m">lagroots.m</A> (Roots of Laguerre polynomials)<LI><A HREF="herroots.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/herroots.m">herroots.m</A> (Roots of Hermite polynomials)</UL><H4>Examples<BR></H4><UL><LI><A HREF="cerfa.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/cerfa.m">cerfa.m </A>(Function file for computingcomplementary error function. BC y(infinity) = 0.<BR>Requires: <A HREF="chebdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/chebdif.m">chebdif.m</A>,<A HREF="chebint.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/chebint.m">chebint.m</A><LI><A HREF="cerfb.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/cerfb.m">cerfb.m</A> (Function file for computing complementaryerror function. BC y(0) = 1<BR>Requires:<A HREF="chebdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/chebdif.m">chebdif.m</A>, <A HREF="chebint.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/chebint.m">chebint.m</A><LI><A HREF="matplot.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/matplot.m">matplot.m</A> (Script file for plotting characteristiccurves of Mathieu's equation)<BR>Requires: <A HREF="fourdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/fourdif.m">fourdif.m</A><LI><A HREF="ce0.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/ce0.m">ce0.m </A>(Function file for computing the Mathieu cosineelliptic function)<BR>Requires: <A HREF="fourdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/fourdif.m">fourdif.m</A>,<A HREF="fourint.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/fourint.m">fourint.m</A><LI><A HREF="sineg.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/sineg.m">sineg.m</A> (Script file for solving the sine-Gordonequation)<BR>Requires: <A HREF="herdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/herdif.m">herdif.m</A>,<A HREF="herroots.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/herroots.m">herroots.m</A>, <A HREF="sincdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/sincdif.m">sincdif.m</A>,<A HREF="fourdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/fourdif.m">fourdif.m</A>, <A HREF="poldif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/poldif.m">poldif.m</A>,<A HREF="sgrhs.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/sgrhs.m">sgrhs.m</A>,<LI><A HREF="sgrhs.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/sgrhs.m">sgrhs.m</A> (Function file for computing the right-handside of the sine-Gordon equation)<LI><A HREF="schrod.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/schrod.m">schrod.m</A> (Script file for computing the eigenvalues of the Schrodinger equation)<BR>Requires:<A HREF="lagdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/lagdif.m">lagdif.m</A>, <A HREF="lagroots.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/lagroots.m">lagroots.m</A>,<A HREF="poldif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/poldif.m">poldif.m</A><LI><A HREF="orrsom.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/orrsom.m">orrsom.m</A> (Script file for computing the eigenvaluesof the Orr-Sommerfeld equation)<BR>Requires: <A HREF="cheb4c.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/cheb4c.m">cheb4c.m</A>, <A HREF="chebdif.m" tppabs="http://ucs.orst.edu/~weidemaj/differ/chebdif.m">chebdif.m</A></UL><P>Last updated: July 4, 2000.</BODY></HTML>?? 快捷鍵說明
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