Berkeley Madonna - возможно самая быстрая и самая удобная программа-решатель дифференциальных уровнений. Программа в настоящее время используется академическими и коммерческими учреждениями для того, чтобы построить математические модели для исследования и обучения.
- 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.
• Two and three-dimensional arrays are now directly supported in the equations. For example, you can write equations like this:
A[1..M,1..N] = k*F[i]+G[i,2,j]
where A is a 2D array, F is a vector (1D array), and G is a 3D array.
• Support for discrete equations (conveyors, ovens, and queues) has been added. They have similar properties to the conveyor, oven, and queue stocks in STELLA; however, some capabilities such as conveyor leakage are not yet supported. Explanatory models can be found in the "How Do I" folder.
• The DELAY built-in function now works properly with zero delay values.
• Discrete functions such as DELAY now work properly when used in array equations. For example, if you have ten signals A through A, a set of delayed signals B through B can be created as follows:
B[1..10] = DELAY(A[i], ...)
• Prime notation now defines a regular equation in addition to automatically-generated differential equations. For example the equation x'' = 2 leads to the following definitions:
x'' = 2
d/dt(x') = x''
d/dt(x) = x'
d/dt(x') = 2
d/dt(x) = x'
• The INF keyword provides a convenient way to represent infinity in your equations.
• The Import Image and Remove Image commands reflect the context in which they are used: if one or more icons are selected, the commands change to Import Icon Image and Remove Icon Image; if no icons are selected, they change to Import Background Image and Remove Background Image.
• Flowchart background images are saved in the model file so they are restored when the model is reopened.
• Flowchart icon images imported using the Import Icon Image command are enlarged or reduced as necessary to prevent the icon from becoming too small or large.
• The Change Color command has been renamed to Background Color to better reflect its purpose.
• Pipes can be hidden independently of flows by unchecking the Pipes box in the Icon Visibility dialog.
• Keyboard shortcuts have been added for the Group and Ungroup commands.
• When programatically selecting an icon (e.g., via the Show Icon command), the flowchart is scrolled as needed so that the icon is visible.
Important: Due to the above changes, flowchart models saved in version 8.0 cannot be opened by previous versions of Berkeley Madonna.
• [Macintosh only] Random number generators were producing erroneous output when running with "fast execution" turned off.
• [Windows only] Program occasionally crashed when using the NETFLOW built-in with arrays of differential equations.
Операционная система: Windows
Язык интерфейса: Английский
Размер: 20,09 мб
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