The method of external excitation for solving generalized Sturm–Liouville problems

A new numerical technique for solving the generalized Sturm–Liouville problem d 2 w d x 2 + q ( x , λ ) w = 0 , b l [ w ( 0 ) , λ ] = b r [ w ( 1 ) , λ ] = 0 is presented. In particular, we consider the problems when the coefficient q ( x , λ ) or the boundary conditions depend on the spectral parameter λ in an arbitrary nonlinear manner. The method presented is based on mathematically modelling the physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the eigenvalues.The results of the numerical experiments justifying the method are presented.