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  2. 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 ...

  3. Collocation - Wikipedia

    en.wikipedia.org/wiki/Collocation

    In 1933, Harold Palmer's Second Interim Report on English Collocations highlighted the importance of collocation as a key to producing natural-sounding language, for anyone learning a foreign language. [11] Thus from the 1940s onwards, information about recurrent word combinations became a standard feature of monolingual learner's dictionaries.

  4. Gauss–Legendre method - Wikipedia

    en.wikipedia.org/wiki/Gauss–Legendre_method

    More specifically, they are collocation methods based on the points of Gauss–Legendre quadrature. The Gauss–Legendre method based on s points has order 2s. [1] All Gauss–Legendre methods are A-stable. [2] The Gauss–Legendre method of order two is the implicit midpoint rule. Its Butcher tableau is:

  5. Collocation extraction - Wikipedia

    en.wikipedia.org/wiki/Collocation_extraction

    Proposed formulas are mutual information, t-test, z test, chi-squared test and likelihood ratio. [1] Within the area of corpus linguistics, collocation is defined as a sequence of words or terms which co-occur more often than would be expected by chance. 'Crystal clear', 'middle management', 'nuclear family', and 'cosmetic surgery' are examples ...

  6. Fractional Chebyshev collocation method - Wikipedia

    en.wikipedia.org/wiki/Fractional_Chebyshev...

    To accomplish this, a fractional differentiation matrix is derived at the Chebyshev Gauss–Lobatto collocation points by using the discrete orthogonal relationship of the Chebyshev polynomials. Then, using two proposed discretization operators for matrix functions results in an explicit form of solution for a system of linear FDEs with ...

  7. Fokas method - Wikipedia

    en.wikipedia.org/wiki/Fokas_method

    The complex collocation points are allowed precisely because of the radiation condition. To capture the endpoint singularities, we expand [ u ] ( x , 0 ) {\displaystyle [u](x,0)} for x ∈ [ − 1 , 1 ] {\displaystyle x\in [-1,1]} in terms of weighted Chebyshev polynomials of the second kind:

  8. General linear methods - Wikipedia

    en.wikipedia.org/wiki/General_linear_methods

    They include multistage Runge–Kutta methods that use intermediate collocation points, as well as linear multistep methods that save a finite time history of the solution. John C. Butcher originally coined this term for these methods and has written a series of review papers, [1] [2] [3] a book chapter, [4] and a textbook [5] on the topic.

  9. Gauss pseudospectral method - Wikipedia

    en.wikipedia.org/wiki/Gauss_pseudospectral_method

    The method is based on the theory of orthogonal collocation where the collocation points (i.e., the points at which the optimal control problem is discretized) are the Legendre–Gauss (LG) points. The approach used in the GPM is to use a Lagrange polynomial approximation for the state that includes coefficients for the initial state plus the ...