Nyström method
In numerical analysis, the Nyström method or quadrature method seeks the numerical solution of an integral equation by replacing the integral with a representative weighted sum. The continuous problem is broken into formula_1 discrete intervals; quadrature or numerical integration determines the weights and locations of representative points for the integral. The problem becomes a system of linear equations with formula_1 equations and formula_1 unknowns, and the underlying function is implicitly represented by an interpolation using the chosen quadrature rule. This discrete problem may be ill-conditioned, depending on the original problem and the chosen quadrature rule. Since the  linear equations require formula_4 operations to solve, high-order quadrature rules perform better because low-order quadrature rules require large formula_1 for a given accuracy. Gaussian quadrature is normally a good choice for smooth, non-singular problems. Discretization of the integral. Standard quadrature methods seek to represent an integral as a weighed sum in the following manner: where formula_7 are the weights of the quadrature rule, and points formula_8 are the abscissas. Example. Applying this to the inhomogeneous Fredholm equation of the second kind results in