Results 121 to 130 of about 3,079 (159)

Solution of inverse nodal problems

Inverse Problems, 1989
We show that the coefficients in a second-order differential equation can be determined from the positions of the nodes for the eigenfunctions. We prove uniqueness results, derive approximate solutions, give error bounds and present numerical experiments.
Hald, Ole H., McLaughlin, Joyce R.
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Inverse nodal problems for singular problems in the half-line

Boletín de la Sociedad Matemática Mexicana, 2023
In this paper, an inverse problem for a singular ordinary differential equation in the half-line is considered. The authors consider a class of positive weights \(\sigma\in L^{1}([0,\infty])\) with \(\int_{0}^{\infty}t\sigma(t ...
Martina Oviedo, Juan Pablo Pinasco
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Approximate solutions of inverse nodal problem with conformable derivative

2023
Summary: Our research is about the Sturm-Liouville equation which contains conformable fractional derivatives of order \(\alpha \in (0,1]\) in lieu of the ordinary derivatives. First, we present the eigenvalues, eigenfunctions, and nodal points, and the properties of nodal points are used for the reconstruction of an integral equation.
Akbarpoor, Shahrbanoo, Dabbaghian, Abdol
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On the well-posedness of the inverse nodal problem

Inverse Problems, 2001
Let \(x_k^{(n ...
Law, C. K., Tsay, Jhishen
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The inverse nodal problem for Hill's equation

Inverse Problems, 2006
Summary: We study the inverse nodal problem for Hill's equation. In particular, we solve the uniqueness, reconstruction and stability problems using the nodal set of periodic (or anti-periodic) eigenfunctions. Furthermore, we show that the space of periodic potential functions \(q\) normalized by \(\int^{1}_{0} q = 0\) is homeomorphic to the partition ...
Cheng, Y. H., Law, C. K.
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A uniqueness theorem for inverse nodal problem

Inverse Problems in Science and Engineering, 2007
In this article, it is found that the asymptotic formulas for nodal points and nodal length for the differential operators having singularity type at the points 0 and π, it is shown that the potential function can be determined from the positions of the nodes for the eigenfunctions.
Hikmet Koyunbakan, Etibar S. Panakhov
openaire   +1 more source

The inverse nodal problem and the Ambarzumyan problem for the p-Laplacian

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2009
We study the issues of the reconstruction and stability 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.
Law, C. K., Lian, Wei-Cheng, Wang, Wei-Chuan   +2 more
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Inverse nodal problems on quantum tree graphs

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2021
We consider inverse nodal problems for the Sturm–Liouville operators on the tree graphs. Can only dense nodes distinguish the tree graphs? In this paper it is shown that the data of dense-nodes uniquely determines the potential (up to a constant) on the tree graphs. This provides interesting results for an open question implied in the paper.
Yang, Chuan-Fu, Liu, Dai-Quan
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Examples of Inverse Nodal Problems

1990
In this talk we will consider the following problem: What can you say about a vibrating rod, if you know the position of the nodes. A node is a point where an eigenfunction vanishes. We will assume that the mass per unit length is constant and try to determine the elasticity of the rod from the nodes. Instead of presenting general theories, (see [1,2,3]
O. H. Hald, J. R. McLaughlin
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A solution of the inverse nodal problem

Inverse Problems, 1997
The author considers the Sturm-Liouville problem \[ - y''+q(x)y=\lambda y, \qquad y(0)\cos\alpha+ y'(0)\sin\alpha=0, \quad y(1)\cos\beta+ y'(1)\sin\beta=0 \] and demonstrates how the potential function \(q(x)\) can be determined from observable eigenfunction nodes when either \(\alpha\) or \(\beta=0\) but not both. This extends work by \textit{O.
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