In mathematics numerical analysis, the Nyström method[1] or quadrature method seeks the numerical solution of an integral equation by replacing the integral with a representative weighted sum.
unknowns, and the underlying function is implicitly represented by an interpolation using the chosen quadrature rule.
[citation needed]operations to solve, high-order quadrature rules perform better because low-order quadrature rules require large
Gaussian quadrature is normally a good choice for smooth, non-singular problems.
Standard quadrature methods seek to represent an integral as a weighed sum in the following manner: where
Applying this to the inhomogeneous Fredholm equation of the second kind results in