• Ordinary Differential Equations
  • Difference Equations
  • 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.
  • 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, stochastic 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. Allows for¬†stochastic modeling using methods such as the Gillespie algorithm.

Import Experimental Data:

  • Curve Fitter - estimate parameters by fitting solution to one or more imported 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.

Some beta features are missing:

We temporarily suppressed some functionality, such as java scripting and histogram plots, present in our beta release due to poor stability. These will be reincorporated in future releases. If your past models used these features and your work requires this functionality, please email MadonnaExec@gmail.com.