Displaying similar documents to “Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials”

Asymptotic analysis of non-self-adjoint Hill operators

Oktay Veliev (2013)

Open Mathematics

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We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L t (q) with a potential q ∈ L 1[0,1] and t-periodic boundary conditions, t ∈ (−π, π]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L 2(−∞,∞) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically...

A note on rapid convergence of approximate solutions for second order periodic boundary value problems

Rahmat A. Khan, Bashir Ahmad (2005)

Archivum Mathematicum

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In this paper, we develop a generalized quasilinearization technique for a nonlinear second order periodic boundary value problem and obtain a sequence of approximate solutions converging uniformly and quadratically to a solution of the problem. Then we improve the convergence of the sequence of approximate solutions by establishing the convergence of order k ( k 2 ) .