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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.
Using step size equal to 1 (h = 1) (Figure 2) Illustration of numerical integration for the equation Blue is the Euler method; green, the midpoint method; red, the exact solution, The step size is
In numerical analysis, the Runge–Kutta methods ( English: / ˈrʊŋəˈkʊtɑː / ⓘ RUUNG-ə-KUUT-tah [1]) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. [2] These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm ...
In numerical analysis, finite-difference methods ( FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time domain (if applicable) are discretized, or broken into a finite number of intervals, and the values of the solution at the end ...
Numerical differentiation. In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.
Cointegration. Cointegration is a statistical property of a collection (X1, X2, ..., Xk) of time series variables. First, all of the series must be integrated of order d (see Order of integration ). Next, if a linear combination of this collection is integrated of order less than d, then the collection is said to be co-integrated.
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