Dymola!

MATLAB is a numerical computing environment and programming language. Maintained by The MathWorks, MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. Although it is numeric only, an optional toolbox uses the MuPAD symbolic engine, allowing access to computer algebra capabilities. An additional package, Simulink, adds graphical multidomain simulation and Model-Based Design for dynamic and embedded systems. »

SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. It is also the name of a very popular conference on scientific programming with Python. The SciPy library depends on NumPy, which provides convenient and fast N-dimensional array manipulation.

Spyder (previously known as Pydee) is a free open-source Python development environment providing MATLAB-like features in a simple and light-weighted software, available for Windows XP/Vista/7, GNU/Linux and Mac OS X.

OpenModelica – A Free Modelica Environment!OpenModelica is an open-source Modelica-based modeling and simulation environment intended for industrial and academic usage. Its long-term development is supported by a non-profit organization – the Open Source Modelica Consortium (OSMC).

Xcos is a graphical editor to design hybrid dynamical systems models. Models can be designed, loaded, saved, compiled and simulated.

Graphical frontend for GNU Octave. Edit formulas in native mathematical notation. Available / tested for Linux x586 / x86_64, WinXP, Vista, and MacOS.

PyDSTool is a sophisticated & integrated simulation and analysis environment for dynamical systems models of physical systems (ODEs, DAEs, maps, and hybrid systems).

Reinteract is a system for interactive experimentation with Python. Reinteract worksheets contain Python code combined with the results of that code, formatted as text or graphical plots. Youu can go back and edit previously entered statements, and the results will update. Reinteract is suitable for experimentation with the Python language and for data analysis using the NumPy and SciPy packages.

SimulationX is an interdisciplinary, multi-domain simulation software for the design, analysis and optimization of complex systems on a single platform. More than 500 ready-to-use model elements and over 300 examples of models from 11 application areas simplify and accelerate the modeling process. Within the shortest time possible, users obtain high-quality results from their simulations. It includes libraries for signal and control, fluids, mechanical 1D/2D/3D, electrics, magnetics, thermal... The advanced user can also develop its own libraries and models since Modelica language is fully supported. SimulationX is best-in-class for generating c-code, standalone executable, dll or s-function. »

Calculation Laboratory is an online environment for numerical computations. By using this site you get fast access to the easy-to-use tool for computing from anywhere. Calculation Lab is perfect for engineering students.

Derive 6.1: Powerful system for doing symbolic and numeric mathematics. This application is no longer available or supported.

Doronix Math Toolbox is a numerical computing environment with programming language which can be used as alternative to MATLAB. It allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user functions, import and export CSV-files and more

Rodeo is a Python IDE for doing data science and analysis natively on your desktop.

20-sim is a modeling and simulation program for mechatronic systems. With 20-sim you can enter model graphically, similar to drawing an engineering scheme. With these models you can simulate and analyze the behavior of multi-domain dynamic systems and create control systems. You can even generate C-code and run this code on hardware for rapid prototyping and HIL-simulation.

The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical programming and optimization. It consists of a language compiler and a stable of integrated high-performance solvers. GAMS is tailored for complex, large scale modeling applications, and allows you to build large maintainable models that can be adapted quickly to new situations. GAMS is specifically designed for modeling linear, nonlinear and mixed integer optimization problems.