# FACSIMILE Introduction

FACSIMILE for Windows is a powerful modelling tool designed to efficiently solve differential equations, with the focus on modelling the kinetics of physical and chemical systems

Over 1,000 licenses have been sold around the world, with many academic institutions using the software as part of their research programs. FACSIMILE for Windows has many benefits:

- Model transport and chemistry problems in a versatile and flexible way.
- Develop useful models rapidly, with specific facilities for modelling chemical kinetics.
- Handle very stiff ordinary differential equations with the robust numerical integrator.
- Understand the results with the easy-to-use visualisation tools

# How FACSIMILE Works

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. FACSIMILE has been designed to solve these extremely stiff problems

efficiently

When solving differential equations numerically, derivations 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 efficiently, even for large problems, by exploiting the sparse nature of the matrices involved.