Numerov's method is a numerical technique used to solve second-order ordinary differential equations, particularly in quantum mechanics and physics. It is based on a finite difference approximation that provides high accuracy for problems with boundary conditions. The method is particularly effective for solving equations where traditional methods may struggle, such as in the case of potential wells. The discussion highlights the importance of understanding the underlying principles of the method for effective application. Overall, Numerov's method is a valuable tool for solving complex differential equations in various scientific fields.