Symbolic semi-discretization of partial differential equation systems

A symbolical computation approach to the preprocessing of distributed parameter systems for preparing a numerical solution by a method of lines technique is investigated. A first prototype of a toolbox for the semi-discretization of partial differential equation systems on simple spatial domains has been implemented in MACSYMA. The equations are classified first in order to support the selection of a particular type of finite difference or spectral methods provided. The resulting differential-algebraic system is either represented symbolically in linear implicit form or in a recursive notation to be passed to an automatic code generation module. Additionally, the semi-discrete system can be analyzed numerically to check its stability properties prior to numerical integration. This way, unsuitable discretizations can be detected and discarded without any simulation experiment. The tool mainly addresses the needs which arise in the analysis of the dynamics of chemical engineering processes.