Ability to calculate integrals of rapidly oscillating functions is crucial for solving many
problems in optics, electrodynamics, quantum mechanics, nuclear physics, and many other
areas. The article considers the method of computing oscillatory integrals using the
transition to the numerical solution of the system of ordinary differential equations. Using the
Levin's collocation method, we reduce the problem to solving a system of linear algebraic
equations. In the case where the phase function has stationary points (its derivative …

Ability to calculate integrals of rapidly oscillating functions is crucial for solving many
problems in optics, electrodynamics, quantum mechanics, nuclear physics, and many other
areas. The article considers the method of computing oscillatory integrals using the
transition to the numerical solution of the system of ordinary differential equations. Using the
Levin's collocation method, we reduce the problem to solving a system of linear algebraic
equations. In the case where the phase function has stationary points,(its derivative …