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applysym.html <!DOCTYPE HTML PUBLIC "-//SQ//DTD HTML 2.0 + all extensions//EN" "hmpro3.dtd"> <HTML> <HEAD> <TITLE></TITLE></HEAD> <BODY> <TABLE BORDER="BORDER"> <TR> <TD>Author</TD> <TD>Thomas Wolf</TD></TR> <TR> <TD>Title</TD> <TD><font face="Courier New">APPLYSYM</font></TD></TR> <TR> <TD>Short description</TD> <TD> The package <font face="Courier New">APPLYSYM</font> takes as input a differential equation (DE) or a system of DEs and its point symmetries, for example computed by the program <a href="liepde.html"><font face="Courier New">LIEPDE</font></a>. It computes symmetry and similarity variables through solving single first order partial DEs (PDEs) with the procedure <font face="Courier New">QUASILINPDE</font></a>. This procedure formulates an equivalent characteristic non-linear system of ordinary DEs (ODEs) which is investigated by the program <a href="crack.html"><font face="Courier New">CRACK</font></a>. Although the program <font face="Courier New">CRACK</font> is primarily made for dealing with overdetermined DE-systems, it nevertheless has good chances of solving the not overdetermined characteristic ODE-systems because <font face="Courier New">CRACK</font> has a number of different integration techniques built in and because Lie-symmetries often have a simple form which results in relatively simple characteristic ODE-systems. The program <font face="Courier New">QUASILINPDE</font></a> can be used independently without connection to symmetries for solving quasi-linear first order PDEs as demonstrated in <font face="Courier New">applysym.tst</font>. </TD></TR> <TR> <TD>Platform</TD> <TD>REDUCE, version 3.6 or 3.7</TD></TR> <TR> <TD>System requirements</TD> <TD>The memory requirements depend crucially on the application. The non-trivial computations in the test file <a href="ftp://ftp.maths.qmw.ac.uk/pub/tw/applysym/applysym.tst"> <font face="Courier New">applysym.tst</font></a> have been run in a 4MB session under LINUX. </TD></TR> <TR> <TD>Installation</TD> <TD>In a running REDUCE session either do <br> <font face="Courier New"> in "applysym.red"$ </font> <br> or, in order to speed up computation, either compile it with <br> <font face="Courier New"> on comp$ </font> <br> before the above command, or, generate a fast-loading compiled file once with <br> <font face="Courier New"> faslout "applysym"$ </font> <br> <font face="Courier New"> in "applysym.red"$ </font> <br> <font face="Courier New"> faslend$ </font> <br> and load that file whenever you want to run <font face="Courier New">APPLYSYM</font> with <br> <font face="Courier New"> load applysym$ </font> <br> In a similar way proceed with the files <font face="Courier New">crack.red, liepde.red</font>. The above commands assume all files to be in the current directory. </TD></TR> <TR> <TD>More information/updates </TD> <TD>There are available a <a href="ftp://ftp.maths.qmw.ac.uk/pub/tw/applysym/applysym.tex">manual</a>, a <a href="ftp://ftp.maths.qmw.ac.uk/pub/tw/applysym/applysym.tst">test file</a> and a <a href="ftp://ftp.maths.qmw.ac.uk/pub/tw/applysym/applysym.rlg">log file</a>. <br> A web demo for <font face="Courier New">APPLYSYM</font> may be available later. The latest version is available from <a href="ftp://ftp.maths.qmw.ac.uk/pub/tw/applysym/"> ftp://ftp.maths.qmw.ac.uk/pub/tw/applysym/</a>. <br> </TD></TR> <TR> <TD>Contact</TD> <TD>e-mail: <a href="mailto:T.Wolf@maths.qmw.ac.uk"> Thomas Wolf</a></TD></TR></TABLE></BODY></HTML>