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  2. Numerical methods for ordinary differential equations

    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.

  3. Midpoint method - Wikipedia

    en.wikipedia.org/wiki/Midpoint_method

    The name of the method comes from the fact that in the formula above, the function giving the slope of the solution is evaluated at = + / = + +, the midpoint between at which the value of () is known and + at which the value of () needs to be found.

  4. Frobenius method - Wikipedia

    en.wikipedia.org/wiki/Frobenius_method

    Some solutions of a differential equation having a regular singular point with indicial roots = and .. In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form ″ + ′ + = with ′ and ″.

  5. 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 ...

  6. 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.

  7. Runge–Kutta–Fehlberg method - Wikipedia

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

    In mathematics, the Runge–Kutta–Fehlberg method (or Fehlberg method) is an algorithm in numerical analysis for the numerical solution of ordinary differential equations. It was developed by the German mathematician Erwin Fehlberg and is based on the large class of Runge–Kutta methods .

  8. 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.

  9. Relaxation (iterative method) - Wikipedia

    en.wikipedia.org/wiki/Relaxation_(iterative_method)

    These equations describe boundary-value problems, in which the solution-function's values are specified on boundary of a domain; the problem is to compute a solution also on its interior. Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [2 ...

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