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Spectral parameter power series method for discontinuous coefficients

Abstract:

Let (a,b) be a finite interval and 1/p, q, r?L1[a,b]. We show that a general solution (in the weak sense) of the equation (pu′)′+qu = λru on (a,b) can be constructed in terms of power series of the spectral parameter λ. 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.