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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. Numerov's method - Wikipedia

    en.wikipedia.org/wiki/Numerov's_method

    Numerov's method (also called Cowell's method) is a numerical method to solve ordinary differential equations of second order in which the first-order term does not appear. It is a fourth-order linear multistep method. The method is implicit, but can be made explicit if the differential equation is linear.

  4. Predictor–corrector method - Wikipedia

    en.wikipedia.org/wiki/Predictor–corrector_method

    In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps:

  5. Runge–Kutta–Fehlberg method - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta–Fehlberg...

    The first row of coefficients at the bottom of the table gives the fifth-order accurate method, and the second row gives the fourth-order accurate method. This shows the computational time in real time used during a 3-body simulation evolved with the Runge-Kutta-Fehlberg method.

  6. Reduction of order - Wikipedia

    en.wikipedia.org/wiki/Reduction_of_order

    Reduction of order (or d’Alembert reduction) is a technique in mathematics for solving second-order linear ordinary differential equations. It is employed when one solution y 1 ( x ) {\displaystyle y_{1}(x)} is known and a second linearly independent solution y 2 ( x ) {\displaystyle y_{2}(x)} is desired.

  7. Trapezoidal rule (differential equations) - Wikipedia

    en.wikipedia.org/wiki/Trapezoidal_rule...

    In numerical analysis and scientific computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidal rule for computing integrals. The trapezoidal rule is an implicit second-order method, which can be considered as both a Runge–Kutta method and a linear multistep method.

  8. Newmark-beta method - Wikipedia

    en.wikipedia.org/wiki/Newmark-beta_method

    The Newmark-beta method is a method of numerical integration used to solve certain differential equations.It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems.

  9. Frobenius solution to the hypergeometric equation - Wikipedia

    en.wikipedia.org/wiki/Frobenius_solution_to_the...

    In the following we solve the second-order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand Georg Frobenius. This is a method that uses the series solution for a differential equation, where we assume the solution takes the form of a series. This is usually the method we use for ...