Berkeley Madonna
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Berkeley Madonna 8.3.18
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Solve differential equations in milliseconds!
Berkeley Madonna is arguably the fastest, most convenient, general purpose differential equation solver available today. It is relatively inexpensive and runs on both Windows and Mac OS. Developed on the Berkeley campus under the sponsorship of NSF and NIH, it is currently used by academic and commercial institutions for constructing mathematical models for research and teaching.
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
- 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.
- 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.
- 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.
- 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
- Use imported data sets as piecewise-linear functions in your model.
- Curve Fitter - estimate parameters by fitting solution to one or more 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.