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

Authors:
S. Yu. Reutskiy
Affiliations:
Science and Technology Center of Magnetism of Technical Objects, The National Academy of Science of Ukraine, Industrialnaya Street,19, 61106, Kharkov, Ukraine
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 4
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Abstract

A new numerical technique for solving the generalized Sturm-Liouville problem d^2wdx^2+q(x,@l)w=0, b"l[w(0),@l]=b"r[w(1),@l]=0 is presented. In particular, we consider the problems when the coefficient q(x,@l) or the boundary conditions depend on the spectral parameter @l 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.