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  2. List of finite element software packages - Wikipedia

    en.wikipedia.org/wiki/List_of_finite_element...

    Software package developed by American and European researchers with the goal to enable automated solution of differential equations: FEniCS Team: 1.6.0: 2015-07-29: LGPL (Core) & GPL/LGPL (Non-Core) [1] Free: Linux, Unix, Mac OS X, Windows: FEATool Multiphysics: MATLAB FEM and PDE multiphysics simulation toolbox: Precise Simulation: 1.10: 2019 ...

  3. Bogacki–Shampine method - Wikipedia

    en.wikipedia.org/wiki/Bogacki–Shampine_method

    The Bogacki–Shampine method is implemented in the ode3 for fixed step solver and ode23 for a variable step solver function in MATLAB (Shampine & Reichelt 1997). Low-order methods are more suitable than higher-order methods like the Dormand–Prince method of order five, if only a crude approximation to the solution is required. Bogacki and ...

  4. Numerical methods for ordinary differential equations - Wikipedia

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

    Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.

  5. List of numerical-analysis software - Wikipedia

    en.wikipedia.org/wiki/List_of_numerical-analysis...

    APMonitor: APMonitor is a mathematical modeling language for describing and solving representations of physical systems in the form of differential and algebraic equations. Armadillo is C++ template library for linear algebra; includes various decompositions, factorisations, and statistics functions; its syntax is similar to MATLAB.

  6. 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.

  7. List of numerical libraries - Wikipedia

    en.wikipedia.org/wiki/List_of_numerical_libraries

    It employs template classes, and has optional links to BLAS and LAPACK. The syntax is similar to MATLAB. Blitz++ is a high-performance vector mathematics library written in C++. Boost.uBLAS C++ libraries for numerical computation; deal.II is a library supporting all the finite element solution of partial differential equations.

  8. Explicit and implicit methods - Wikipedia

    en.wikipedia.org/wiki/Explicit_and_implicit_methods

    In the vast majority of cases, the equation to be solved when using an implicit scheme is much more complicated than a quadratic equation, and no analytical solution exists. Then one uses root-finding algorithms, such as Newton's method, to find the numerical solution. Crank-Nicolson method. With the Crank-Nicolson method

  9. Boundary element method - Wikipedia

    en.wikipedia.org/wiki/Boundary_element_method

    The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form), including fluid mechanics, acoustics, electromagnetics (where the technique is known as method of moments or abbreviated as MoM), [1] fracture mechanics, [2] and contact mechanics.

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