Radau

Radau is a term that appears in multiple domains. In mathematics and numerical analysis, Radau denotes a class of orthogonal polynomials and associated quadrature rules. Gauss–Radau quadrature is a numerical integration method on a finite interval that uses one endpoint of the interval as a node, along with additional interior nodes chosen to maximize the degree of exactness. The nodes of Gauss–Radau quadrature are called Radau points, and the corresponding weights are computed to ensure exact integration of polynomials up to a certain degree. Radau polynomials refer to the family of orthogonal polynomials used to construct these quadrature rules and play a role in spectral and finite element methods. The Radau family is related to other classical families such as Legendre and Jacobi polynomials but is distinguished by its endpoint node.

The term Radau also appears in non-mathematical contexts as a surname of German origin and as a toponym in German-speaking regions, where it is used in names of towns, rivers, and geographic features. It may appear in historical documents, literature, and contemporary datasets.

In summary, Radau primarily denotes important ideas in numerical integration and orthogonal polynomials, with additional use as a geographic and personal name. The concept is widely used in applied mathematics, physics, and engineering for accurate discretization of integrals and differential equations.