text: From the mathematical point of view the Lippmann–Schwinger equation in coordinate representation is an integral equation of Fredholm type. It can be solved by discretization. Since it is equivalent to the differential time-independent Schrödinger equation with appropriate boundary conditions, it can also be solved by numerical methods for differential equations. In the case of the spherically symmetric potential  it is usually solved by partial wave analysis. For high energies and/or weak potential it can also be solved perturbatively by means of Born series. The method convenient also in the case of many-body physics, like in description of atomic, nuclear or molecular collisions is the method of R-matrix of Wigner and Eisenbud. Another class of methods is based on separable expansion of the potential or Green's operator like the method of continued fractions of Horáček and Sasakawa. Very important class of methods is based on variational principles, for example the Schwinger-Lanczos method combining the variational principle of Schwinger with Lanczos algorithm.