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


  • 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.