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  2. Numerical methods for ordinary differential equations - Wikipedia

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

    The step size is =. The same illustration for = The midpoint method converges faster than the Euler method, as .. Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).

  3. 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.

  4. Predictor–corrector method - Wikipedia

    en.wikipedia.org/wiki/Predictor–corrector_method

    When considering the numerical solution of ordinary differential equations (ODEs), a predictor–corrector method typically uses an explicit method for the predictor step and an implicit method for the corrector step.

  5. Euler method - Wikipedia

    en.wikipedia.org/wiki/Euler_method

    The next step is to multiply the above value by the step size , which we take equal to one here: = = Since the step size is the change in , when we multiply the step size and the slope of the tangent, we get a change in value.

  6. Dormand–Prince method - Wikipedia

    en.wikipedia.org/wiki/Dormand–Prince_method

    Dormand–Prince is the default method in the ode45 solver for MATLAB [4] and GNU Octave [5] and is the default choice for the Simulink's model explorer solver. It is an option in Python's SciPy ODE integration library [6] and in Julia's ODE solvers library. [7] Implementations for the languages Fortran, [8] Java, [9] and C++ [10] are also ...

  7. Euler–Maruyama method - Wikipedia

    en.wikipedia.org/wiki/Euler–Maruyama_method

    In Itô calculus, the Euler–Maruyama method (also simply called the Euler method) is a method for the approximate numerical solution of a stochastic differential equation (SDE). It is an extension of the Euler method for ordinary differential equations to stochastic differential equations named after Leonhard Euler and Gisiro Maruyama. The ...

  8. Collocation method - Wikipedia

    en.wikipedia.org/wiki/Collocation_method

    In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...

  9. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]