An inverse nodal problem consists in reconstructing this operator from the given zeros of their eigenfunctions. In this work, we are concerned with the inverse nodal problem of the Sturm-Liouville operator with eigenparameter dependent boundary conditions on a finite interval. We prove uniqueness theorems: a dense subset of nodal points uniquely determine the parameters of the boundary conditio...

abstract: in this paper, a new population-based search called the bees algorithm (ba) is presented to estimate the time-dependent heat transfer coefficient and the corresponding heat flux at the boundaries of a two-dimensional body subjected to transient heat conduction, using the temperature measurements at discrete nodal locations on the boundaries, where heat flux is specified as the boundar...

Inverse spectral problems consist in recovering operators from their spectral characteristics. Such problems play an important role in mathematics and have many applications in natural sciences (see, for example, [1 – 6]). In 1988, the inverse nodal problem was posed and solved for Sturm-Liouville problems by J. R. McLaughlin [7], who showed that the knowledge of a dense subset of nodal points ...

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.

We study the issues of reconstruction and stability issues of the inverse nodal problem for the one-dimensional p-Laplacian eigenvalue problem. A key step is the application of a modified Prüfer substitution to derive a detailed asymptotic expansion for the eigenvalues and nodal lengths. Two associated Ambarzumyan problems are also solved. AMS Subject Classification (2000) : 34A55, 34B24. 1 2 1...

In this paper, the inverse problem of recovering the potential function, on a general finite interval, of a singular Sturm–Liouville problem with a new spectral parameter, called the nodal point, is studied. In addition, we give an asymptotic formula for nodal points and the density of the nodal set. c © 2006 Elsevier Ltd. All rights reserved.

The inverse nodal problem was initiated by McLaughlin [1], who proved that the Sturm-Liouville problem is uniquely determined by any dense subset of the nodal points. Some numerical schemes were given by Hald and McLaughlin [2] for the reconstruction of the potential. Recently Law, Yang and other authors have reconstructed the potential function and its derivatives of the Sturm-Liouville proble...