Gauss–Legendre methods are a family of numerical methods for ordinary differential equations. Gauss–Legendre methods are implicit Runge–Kutta methods...

for integrals. The Gauss–Legendre methods use the points of Gauss–Legendre quadrature as collocation points. The Gauss–Legendre method based on s points...

In numerical analysis, Gauss–Legendre quadrature is a form of Gaussian quadrature for approximating the definite integral of a function. For integrating...

collocation methods. The Gauss–Legendre methods form a family of collocation methods based on Gauss quadrature. A Gauss–Legendre method with s stages...

&1/2&1/2\\\end{array}}} These methods are based on the points of Gauss–Legendre quadrature. The Gauss–Legendre method of order four has Butcher tableau:...

The Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing...

gravitational constant and the method of least squares, which he had discovered before Adrien-Marie Legendre published it. Gauss was in charge of the extensive...

theory completed that of Legendre. He developed, and first communicated to his contemporaries before Gauss, the least squares method which has broad application...

a priority dispute with Legendre. However, to Gauss's credit, he went beyond Legendre and succeeded in connecting the method of least squares with the...

Gauss–Legendre algorithm Gauss–Legendre method Gauss–Legendre quadrature Legendre (crater) Legendre chi function Legendre duplication formula Legendre–Papoulis...

as "row reduction" or "Gaussian method" Gauss–Jordan elimination Gauss–Seidel method Gauss's cyclotomic formula Gauss's lemma in relation to polynomials...

The Gauss pseudospectral method (GPM), one of many topics named after Carl Friedrich Gauss, is a direct transcription method for discretizing a continuous...

polynomials of degree 2n − 1 or less. This exact rule is known as the Gauss–Legendre quadrature rule. The quadrature rule will only be an accurate approximation...

International Space Station. There are three basic types of Legendre pseudospectral methods: One based on Gauss-Lobatto points First proposed by Elnagar et al and...

In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number...

fourth-order method Runge–Kutta–Fehlberg method — a fifth-order method with six stages and an embedded fourth-order method Gauss–Legendre method — family...

latitude of the vertices (in place of a spherical radius). Gauss provided more exact formulae. Legendre (1798). Delambre (1798). Tropfke (1903). Buzengeiger...

quadratic reciprocity theorem was conjectured by Euler and Legendre and first proved by Gauss, who referred to it as the "fundamental theorem" in his Disquisitiones...

pseudospectral knotting method, the flat pseudospectral method, the Legendre-Gauss-Radau pseudospectral method and pseudospectral methods for infinite-horizon...

of the AGM algorithms. Landen's transformation Gauss–Legendre algorithm Generalized mean By 1799, Gauss had two proofs of the theorem, but neither of them...

integrated against Legendre polynomials in a Chebyshev series and then converting to a Legendre series. A major advantage of the method in this scenario...

from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss (under the pseudonym of Monsieur LeBlanc). One of the pioneers of...

Poore (2014), "Orbit and uncertainty propagation: a comparison of Gauss–Legendre-, Dormand–Prince-, and Chebyshev–Picard-based approaches", Celestial...

tool using Romberg, Fox–Romberg, Gauss–Legendre and other numerical methods SciPy implementation of Romberg's method Romberg.jl — Julia implementation...

basis. The method gains its efficiency by placing the nodal points at the Legendre-Gauss-Lobatto (LGL) points and performing the Galerkin method integrations...

semigroup of all the integers. One advantage of this notation over Gauss's is that the Legendre symbol is a function that can be used in formulas. It can also...

In numerical analysis, Gauss–Jacobi quadrature (named after Carl Friedrich Gauss and Carl Gustav Jacob Jacobi) is a method of numerical quadrature based...

case of the gamma function, notably a table computed by Gauss in 1813 and one computed by Legendre in 1825. Tables of complex values of the gamma function...

regression was the method of least squares, which was published by Legendre in 1805, and by Gauss in 1809. Legendre and Gauss both applied the method to the problem...

control, a term coined by Ross. Unlike the Legendre pseudospectral method, the Chebyshev pseudospectral (PS) method does not immediately offer high-accuracy...