ConLaw

Title | CONLAW
Author | Thomas Wolf
Short description | The package CONLAW computes first integrals of ordinary differential equations (ODEs) or conservation laws (CLs) of partial differential equations (PDEs) or systems of both. Four different approaches to compute CLs have been implemented in four different programs CONLAW1 ... CONLAW4. All use the program CRACK to solve the overdetermined system of conditions they generate and all four versions use a set of common routines placed in the file conlaw0.red.
Platform | REDUCE, version 3.6, 3.7 or 3.8
System requirements | The memory requirements depend crucially on the application. For example, the non-trivial computations in the test file conlaw.tst have been run in a 8MB session under LINUX. But it is not difficult to increase memory requirements indefinitely by simply increasing the order of the conservation laws of PDEs that are to be computed.
Installation | In a running REDUCE session either do in "conlaw0.red"$ or, in order to speed up computation, either compile it with on comp$ before the above command, or, generate a fast-loading compiled file once with faslout "conlaw0"$ in "conlaw0.red"$ faslend$ and load that file whenever you want to run CONLAW with load conlaw0$ In a similar way proceed with crack.red and with conlaw1.red,...,conlaw4.red depending on which of the 4 approaches shall be applied. The above commands assume all files to be in the current directory.
More information/updates | There are available a manual, a test file and a log file. A detailed comparison of the four methods is given in Wolf, T.: A comparison of four approaches to the calculation of conservation laws, Euro. Jnl of Appl. Math., 13, part 2 (2002) 129-152. available as arxiv preprint cs.SC/0301027 and as dvi, ps and pdf file. More related to the computer algebraic issues is the paper Wolf, T., Brand, A., Mohammadzadeh, M.: Computer algebra algorithms and routines for the computation of conservation laws and fixing of gauge in differential expressions, J. Symb. Comp. 27 (1999), 221-238. available as dvi, ps and pdf file. CONLAW can be run from a web demo created by Francis Wright and Arrigo Triulzi with problems of restricted size. The latest version is available from http://lie.math.brocku.ca/crack/src/.
Contact | e-mail: Thomas Wolf