FACSIMILE

FACSIMILE Methods

Many processes involve the evolution in time of a system defined by non-linear differential equations. The values of variables are controlled by equations which define the rate of change of these variables in terms of their values. There may be many variables, with widely different numerical values.

These problems often have a property called stiffness - the system has some solutions that change very rapidly compared with other solutions, or some solutions which change very rapidly at some times and slowly at other times. Many numerical packages have difficulty coping with stiffness. FACSIMILE, however, has been designed to solve efficiency extremely stiff problems. It has been carefully tuned on demanding problems over many years, using a sophisticated version of Gear's method as the basic algorithm.

When solving differential equations numerically, derivatives are replaced by differences over a finite time step. FACSIMILE uses a predictor-corrector technique, in which the values of the solution vector at the end of a step are first predicted, and are then corrected to satisfy the differential equations by a few Newton iterations. FACSIMILE does this efficiency, even for large problems, by exploiting the sparse nature of the matrices involved.

FACSIMILE provides a powerful package to model complex reaction schemes, and is designed to be simple to use. Complex reaction schemes are readily coded using FACSIMILE's high-level programming notation which was purpose designed for stating the problem as a chemist would describe it. The problem is then submitted to the FACSIMILE solver which copes with all the mathematical aspects of the solution using robust, proven, efficient numerical methods.

The high level FACSIMILE language simplifies the initial writing and later adaption of the model to new problems of interest. FACSIMILE relieves the modelling of the difficulty of determining the best numerical method, remains robust and reliable and leaves him/her free to concentrate on the results.

FACSIMILE is particularly suitably for those problems where local reactions between different solution components tend to dominate advective transport.