Skip Navigation Linksberkeley-madonna



Berkeley Madonna 動態模型軟體


Berkeley Madonna 可以說是現今最快,最方便,最通用的微分方程求解軟體。而且它相對便宜,並可運行在 Windows 和Mac OS。費長適合用於學術和商業機構構建數學模型,研究和教學。


  • 常微分方程 - 初始條件和邊值問題
  • 差分方程 - 初始條件和邊值問題
  • 多維代數方程根求解


  • 以任意順序排列數學方程式與符號,亦可從 STELLA 方程式文件導入方程。
  • 點擊運行。解決方案自動生成。工具欄上的按鈕變量透過圖形來做切換。


  • 流程編輯器–利用圖標直觀地創建模型,讓程式自動生成方程式。
  • 化學反應 - 編寫傳統的化學符號化學方程式。程式將自動應用相應的速率定律,並為您生成動力方程。


  • Berkeley Madonna 的驚人速度使得它適合大型系統,邊值問題,蒙特卡羅模型,曲線擬合,求根,批量處理,參數曲線,剛性系統,等等。

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. 


  • 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.