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  2. List of open-source software for mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_open-source...

    The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .

  3. List of finite element software packages - Wikipedia

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

    BE, CN, and Fractional-Step-Theta schemes Predefined equations: Incompressible Navier-Stokes, heat transfer, convection-diffusion-reaction, linear elasticity, electromagnetics, pressure acoustics, Darcy's law, and support for custom PDE equations Miniapps and examples for Laplace, elasticity, Maxwell, Darcy, advection, Euler, Helmholtz, and others

  4. Xcas - Wikipedia

    en.wikipedia.org/wiki/Xcas

    Xcas can solve equation, calculate derivative, antiderivative and more. Figure 3. Xcas can solve differential equations. Xcas is a user interface to Giac, which is an open source [2] computer algebra system (CAS) for Windows, macOS and Linux among many other platforms. Xcas is written in C++. [3] Giac can be used directly inside software ...

  5. Differential equation - Wikipedia

    en.wikipedia.org/wiki/Differential_equation

    The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.

  6. 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.

  7. Spectral method - Wikipedia

    en.wikipedia.org/wiki/Spectral_method

    Here we presume an understanding of basic multivariate calculus and Fourier series.If (,) is a known, complex-valued function of two real variables, and g is periodic in x and y (that is, (,) = (+,) = (, +)) then we are interested in finding a function f(x,y) so that

  8. Linear multistep method - Wikipedia

    en.wikipedia.org/wiki/Linear_multistep_method

    Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point. The process continues with subsequent steps to map out the solution.

  9. MacCormack method - Wikipedia

    en.wikipedia.org/wiki/MacCormack_method

    The application of MacCormack method to the above equation proceeds in two steps; a predictor step which is followed by a corrector step. Predictor step: In the predictor step, a "provisional" value of u {\displaystyle u} at time level n + 1 {\displaystyle n+1} (denoted by u i p {\displaystyle u_{i}^{p}} ) is estimated as follows

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