## Features

See What's New in Version 8.0 for a list of changes and additions since Madonna 6.0.

### Solves:

- Ordinary Differential Equations - initial conditions and boundary value problems
- Difference Equations - initial conditions and boundary value problems
- Multi-dimensional transcendental algebraic equation roots
- Discrete simulations using conveyors, ovens, and queues

### Easy to Use:

- Type equations directly into equation window in ordinary mathematical notation, in any order; or, import equations from STELLA equation files.
- Click Run. Solutions are automatically plotted. Buttons on toolbar allow variables to be toggled on and off the graph.

### Special Interfaces:

- Flowchart Editor - create models visually with icons and let Berkeley Madonna write the equations.
- Chemical Reactions - write chemical equations using conventional chemical notation. Berkeley Madonna will automatically apply the appropriate rate law (e.g., mass action) and generate kinetic equations for you.

### Very Fast Execution:

- Berkeley Madonna's impressive speed makes it suitable for large-scale systems, boundary value problems, Monte Carlo models, curve fitting, root finding, batch processes, parameter plots, stiff systems, etc.

### Parameter Exploration:

- Change parameter values directly using the parameter window.
- Parameter Sliders - move the slider and the model runs instantly and displays the new solution.
- Automatic Scan of Parameter Space - define a range for a parameter and Berkeley Madonna computes and plots a family of curves spanning the range.
- Parameter Plots - select an attribute (min, max, mean, frequency, etc.) of any variable. Berkeley Madonna automatically plots the attribute as a function of a parameter.
- Sensitivity Analysis - plots the partial derivative of any variable with respect to any parameter.
- Optimization - searches the parameter space for a point that minimizes an arbitrary expression.

### Integration Algorithms:

- Euler (1st-order)
- Runge-Kutta (2nd and 4th order)
- Adaptive stepsize (4th order Runge-Kutta)
- Stiff ODE solver (Rosenbrock)
- Custom DT - write your own equations for adjusting stepsize

### Import Experimental Data:

- Use imported data sets as piecewise-linear functions in your model.
- Curve Fitter - estimate parameters by fitting solution to one or more data sets

### Other Capabilities:

- Fast Fourier Transform - plot results in frequency domain.
- Array notation (dimensioned variables)
- Hybrid multi-dimensional root solver used to automatically set up steady-state initial conditions. Can also be embedded in integration loops.

### Intuitive Interface:

### Phase Plane (X-Y) Plots:

### Oscilloscope Plots:

Normal plot

Oscilloscope Plot

User-defined triggers reset plot to time zero.