Spectral parameter power series for Sturm-Liouville problems

Details Spectral parameter power series for Sturm-Liouville problems Spectral parameter power series for Sturm-Liouville problems

2008-11-28

arxiv.org/abs/0811.4488v1

Mathematical Methods in the Applied Sciences, 2010, v. 33, issue 4, 459-468

Physics

Mathematical Physics

Scientific paper

We consider a recently discovered representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS). The coefficients of the power series are given in terms of a particular solution of the Sturm-Liouville equation with the zero spectral parameter. We show that, among other possible applications, this provides a new and efficient numerical method for solving initial value and boundary value problems. Moreover, due to its convenient form the representation lends itself to numerical solution of spectral Sturm-Liouville problems, effectively by calculation of the roots of a polynomial. We discuss examples of the numerical implementation of the SPPS method and show it to be equally applicable to a wide class of singular Sturm-Liouville problems as well as to problems with spectral parameter dependent boundary conditions.

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