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  2. Numerical methods for ordinary differential equations - Wikipedia

    en.wikipedia.org/wiki/Numerical_methods_for...

    methods for second order ODEs. We said that all higher-order ODEs can be transformed to first-order ODEs of the form (1). While this is certainly true, it may not be the best way to proceed. In particular, Nyström methods work directly with second-order equations.

  3. MATLAB - Wikipedia

    en.wikipedia.org/wiki/MATLAB

    MATLAB (an abbreviation of "MATrix LABoratory" [18]) 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.

  4. GNU Octave - Wikipedia

    en.wikipedia.org/wiki/GNU_Octave

    GNU Octave is a scientific programming language for scientific computing and numerical computation.Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB.

  5. FEATool Multiphysics - Wikipedia

    en.wikipedia.org/wiki/FEATool_Multiphysics

    FEATool Multiphysics is a fully integrated physics and PDE simulation environment where the modeling process is subdivided into six steps; preprocessing (CAD and geometry modeling), mesh and grid generation, physics and PDE specification, boundary condition specification, solution, and postprocessing and visualization.

  6. Ordinary differential equation - Wikipedia

    en.wikipedia.org/wiki/Ordinary_differential_equation

    COPASI, a free (Artistic License 2.0) software package for the integration and analysis of ODEs. MATLAB, a technical computing application (MATrix LABoratory) GNU Octave, a high-level language, primarily intended for numerical computations. Scilab, an open source application for numerical computation.

  7. Finite difference method - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_method

    For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).

  8. List of programming languages for artificial intelligence

    en.wikipedia.org/wiki/List_of_programming...

    These toolboxes provide APIs for the high-level and low-level implementation and use of many types of machine learning models that can integrate with the rest of the MATLAB ecosystem. These libraries also have support for code generation for embedded hardware. C++ is a compiled language that can interact with low-level hardware.

  9. Numerical continuation - Wikipedia

    en.wikipedia.org/wiki/Numerical_continuation

    The same terminology applies. A regular solution is a solution at which the Jacobian is full rank (). A singular solution is a solution at which the Jacobian is less than full rank. A regular solution lies on a k-dimensional surface, which can be parameterized by a point in the tangent space (the null space of the Jacobian).

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