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MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
SymPy, a Python package that can solve ODEs symbolically Julia (programming language) , a high-level language primarily intended for numerical computations. SageMath , an open-source application that uses a Python-like syntax with a wide range of capabilities spanning several branches of mathematics.
Full API for Java and Matlab (the latter via add-on product) PyMFEM (Python) Python, Scilab or Matlab Python bindings to some functionality Python Other: Predefined equations: Yes, many predefined physics and multiphysics interfaces in COMSOL Multiphysics and its add-ons. A large number of Bilinear and Linear forms
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly.
Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations.
Shogun, an open-source large-scale machine-learning toolbox that provides several SVM implementations (like libSVM, SVMlight) under a common framework and interfaces to Octave, MATLAB, Python, R; Waffles is a free-software collection of command-line tools designed for scripting machine-learning operations in automated experiments and processes.
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SymPy is an open-source Python library for symbolic computation.It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3]