Introduction
PDESOL solves 1-D systems of partial and ordinary differential equations (ODE/PDEs).
PDESOL was designed with the objective of minimizing the amount of effort it takes to
specify, solve, and visualize the solution of a system of partial differential equations
without sacrificing power and flexibility.
The pdesol Graphical User Interface (GUI) helps with the navigation of options and
commands by following standard Windows conventions. The pdesol input language closely
resembles the mathematical notation used to write systems of differential equations and
relieves the user of the burden of having to work with arrays, indexes, subroutine calls
to solvers, and so on. For maximum power and flexibility, you can easily include
algebraic, tabular, conditional expressions, and several built-in functions in the problem
statement.
PDESOL provides a self-contained computing environment for the solution of systems of
partial differential equations, without the need for external compilation of source code.
After specifying the system of equations in the Equations
Window, you are ready to solve it. The method of solution is based on the numerical
method of lines (MOL), where spatial derivatives are approximated by finite differences
and the resulting set of ODEs are integrated with robust integrators such as LSODES and
RKF45. By taking advantage of the choice of integrators and spatial differentiation
routines, you can obtain the optimum numerical approximation depending on the nature of
the problem (e.g., stiff system of equations, convective characteristics, etc.). The
PDESOL Help file includes extensive guidelines to take maximum advantage of these options.
PDESOL has several tools to help users visualize the solution. Using dialog boxes, the
user specifies the view and pdesol retrieves and displays the results using default
formats. pdesol includes two windows to visualize the solution: the Table
Window and the Chart Window. The Table Window is
actually a spreadsheet, offering powerful post-processing options to perform additional
calculations on the problem solution. A wide range of formatting options is also available
for tables and charts, as well as exporting/importing capabilities to share tables and
charts with other applications.
PDESOL can solve linear and nonlinear systems of up to 50 ODE/PDEs with a maximum of 1001
grid points in the spatial direction. The equations should be first order in time (t) and
can be up to fourth order in space (x).
Application examples include the well known PDE test problems: Burgers' equation, the
cubic Schroedinger equation and the Korteweg - de Vries equation. The details for viewing
these applications, as well as a thorough discussion of the mathematical concepts on which
the applications and the numerical algorithms are based, are included in the Tutorial of
the Help menu.
A wide range of engineering problems is also included in the application examples
provided with the demonstration package.
PDESOL is well suited for applications involving the dynamic modeling of transport process
systems.
For additional questions or comments, send e-mail to: support@pdesol.com
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