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arXiv · 1405.5632

Spectral parameter power series method for discontinuous coefficients

Herminio Blancarte·Hugo M. Campos·Kira V. Khmelnytskaya
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Abstract

Let (a,b) be a finite interval and 1/p, q, r be functions from L1(a,b). We show that a general solution (in the weak sense) of the equation (pu')'+qu = zru on (a,b) can be constructed in terms of power series of the spectral parameter z. The series converge uniformly on [a,b] and the corresponding coefficients are constructed by means of a simple recursive procedure. We use this representation to solve different types of eigenvalue problems. Several numerical tests are discussed.

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Herminio Blancarte, Hugo M. Campos, Kira V. Khmelnytskaya. 2014-05-22. Spectral parameter power series method for discontinuous coefficients. https://doi.org/10.1002/mma.3282

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