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- 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.
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.
- 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.
- 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.
- 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.