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: supportATSIGNpdesolDOTcom

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