USFKAD: An expert system for partial differential equations

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 summaryTitle of program:USFKADCatalogue identifier:ADYN_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYN_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:noneOperating systems under which the program has been tested: Windows, UNIXProgramming language used:C++, LaTeXNo. of lines in distributed program, including test data, etc.: 11 699No. of bytes in distributed program, including test data, etc.: 537 744Memory required to execute with typical data: 1.3 MegabytesDistribution format: tar.gzNature of mathematical problem: Analytic solution of Poisson, diffusion, and wave equationsMethod of solution: Eigenfunction expansionsRestrictions 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 secondUnusual 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.