Nyström method
Encyclopedia
The Nyström method of discretizing
an integral equation
uses a quadrature rule
; i.e. applying the quadrature rule
to, for example, the inhomogeneous Fredholm equation of the second kind
,
results in
.
Discretization
In mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers...
an integral equation
Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way...
uses a quadrature rule
Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of...
; i.e. applying the quadrature rule
to, for example, the inhomogeneous Fredholm equation of the second kind
,results in
.