Computer Physics Communications Program Library

Programs in Physics & Physical Chemistry



Manuscript Title: Similarity solutions of partial differential equations using DESOLV
Authors: K. T. Vu, J. Butcher, J. Carminati
Program title: DESOLV
Catalogue identifier: ADYZ_v1_0 Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 176(2007)682
Programming language: Maple internal language.
Computer: Platforms supported by the Maple (version 9 or higher) computer algebra system.
Operating system: Linux, Windows XP.
RAM: Dependent on problem (small ≈ MB, large ≈ GB).
Word size: Dependent on Maple distribution (supports 32 and 64 bit platforms)
Keywords: Similarity solutions, computer algebra, differential equations.
PACS: 02.70.Wz, 02.30.Jr, 02.20.Tw.
Classification: 4.3, 5.
Nature of problem: Systems of differential equations occur often in many theoretical and applied areas. In many cases, exact solutions are required as numerical methods are not appropriate or applicable. Indeed, exact solutions of systems of partial differential equations arising in fluid dynamics, continuum mechanics and general relativity are of considerable value for the light they shed into extreme cases which are not susceptible to numerical treatments. One important source of exact solutions to differential equations is the application of the group theoretic method of Lie. Such solutions found by Lie's method, are called invariant solutions. Essential to this approach is the need to solve overdetermined systems of "determining equations", which consist of coupled, linear, homogeneous, partial differential equations. Typically, such systems vary between ten to several hundred equations. Clearly in the case of sets of equations consisting of about 100 equations or more, the prospect of finding solutions to such systems with just pencil and paper would certainly be quite daunting. DESOLV, which runs under Maple, attempts to automate as much as possible the process of determining these invariant solutions. The program has modular structure and not only uses basic features of Maple but has independently built-in routines to augment or assist.
Solution method: See "Nature of problem", above.
Restrictions: Sufficient amount of memory and the nature of the determining system of equations.
Running time: Dependent on problem (small ≈ second, large ≈ hours).