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

A new numerical technique for solving the generalized Sturm–Liouville problem d2wdx2+q(x,λ)w=0, bl[w(0),λ]=br[w(1),λ]=0bl[w(0),λ]=br[w(1),λ]=0 is presented. In particular, we consider the problems when the coefficient q(x,λ)q(x,λ) or the boundary conditions depend on the spectral parameter λλ 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.