USFKAD: An expert system for partial differential equations

Abstract

The computation of the solution, by the separation of variables process, of the Poisson, diffusion, and wave equations in rectangular, cylindrical, or spherical coordinate systems, with Dirichlet, Neumann, or Robin boundary conditions, can be carried out in the time, Laplace, or frequency domains by a decision-tree process, using a library of eigenfunctions. We describe an expert system, USFKAD, that has been constructed for this purpose. Program summary Title of program:USFKAD Catalogue identifier:ADYN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYN_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Operating systems under which the program has been tested: Windows, UNIX Programming language used:C++, LaTeX No. of lines in distributed program, including test data, etc.: 11 699 No. of bytes in distributed program, including test data, etc.: 537 744 Memory required to execute with typical data: 1.3 Megabytes Distribution format: tar.gz Nature of mathematical problem: Analytic solution of Poisson, diffusion, and wave equations Method of solution: Eigenfunction expansions Restrictions concerning the complexity of the problem: A few rarely-occurring singular boundary conditions are unavailable, but they can be approximated by regular boundary value problems to arbitrary accuracy. Typical running time:1 second Unusual features of the program: Solutions are obtained for Poisson, diffusion, or wave PDEs; homogeneous or nonhomogeneous equations and/or boundary conditions; rectangular, cylindrical, or spherical coordinates; time, Laplace, or frequency domains; Dirichlet, Neumann, Robin, singular, periodic, or incoming/outgoing boundary conditions. Output is suitable for pasting into LaTeX documents.