Solution of inverse nodal problems

Hald, Ole H.; McLaughlin, Joyce R.

doi:10.1088/0266-5611/5/3/008

Cited by 162 publications

(106 citation statements)

References 12 publications

Supporting

Mentioning

102

Contrasting

Unclassified

Order By: Relevance

“…The data indicates quadratic convergence away from the discontinuity, which is consistent with our observations in [HMcL2]. n = 5 n = 10 n = 20 n = 40 Table 2.…”

Section: Section 5: Numerical Experimentssupporting

confidence: 89%

Inverse problems: recovery of BV coefficients from nodes

Hald

McLaughlin

1998

Inverse Problems

View full text Add to dashboard Cite

We consider the Sturm-Liouville problem on a finite interval with Dirichlet boundary conditions. Let the elastic modulus and the density be of bounded variation. Results for both the forward problem and the inverse problem are established. For the forward problem, new bounds are established for the eigenfrequencies. The bounds are sharp. For the inverse problem, it is shown that the elastic modulus is uniquely determined, up to one arbitrary constant, by a dense subset of the nodes of the eigenfunctions when the density is known. Similarly it is shown that the density is uniquely determined, up to one arbitrary constant, by a dense subset of the nodes of the eigenfunctions when the elastic modulus is known. Algorithms for finding piecewise constant approximations to the unknown elastic modulus or density are established and are shown to converge to the unknown function at every point of continuity. Results from numerical calculations are presented.

show abstract

“…The data indicates quadratic convergence away from the discontinuity, which is consistent with our observations in [HMcL2]. n = 5 n = 10 n = 20 n = 40 Table 2.…”

Section: Section 5: Numerical Experimentssupporting

confidence: 89%

Inverse problems: recovery of BV coefficients from nodes

Hald

McLaughlin

1998

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…She showed that the knowledge of a dense subset of nodal points is su¢ cient to determine the potential function of Sturm-Liouville problem up to a constant [21]. Also, some numerical results about this problem were given in [22]. Nowadays, many authors have given some interesting results about inverse nodal problems for di¤erent type operators (see [23], [24], [25], [26], [27]).…”

Section: Introductionmentioning

confidence: 99%

Inverse nodal problem for p_Laplacian diffusion equation with polynomially dependent spectral parameter

YILMAZ¹

2016

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

View full text Add to dashboard Cite

INVERSE NODAL PROBLEM FOR p LAPLACIAN DIFFUSION EQUATION WITH POLYNOMIALLY DEPENDENT SPECTRAL PARAMETER TUBA GULSEN AND EMRAH YILMAZAbstract. In this study, solution of inverse nodal problem for one-dimensional p-Laplacian di¤usion equation is extended to the case that boundary condition depends on polynomial eigenparameter. To …nd the spectral datas as eigenvalues and nodal parameters of this problem, we used a modi…ed Prüfer substitution. Then, reconstruction formula of the potential function is also given by using nodal lenghts. Furthermore, this method is similar to used in [1], our results are more general.(Dedicated to Prof. E. S. Panakhov on his 60-th birthday)

show abstract

“…Such problems play an important role in mathematics and have many applications in natural sciences and engineering (see [1,2,15,[20][21][22]29] and the references therein). The inverse nodal problem, first posed and solved by McLaughlin [13,23], is the problem of constructing operators from given nodes (zeros) of their eigenfunctions (refer to [3][4][5]12,14,17,24,[26][27][28]). From the physical point of view this corresponds to finding, e.g., the density of a string or a beam from the zero-amplitude positions of their eigenvibrations.…”

Section: Introductionmentioning

confidence: 99%

Inverse Nodal Problem for Dirac Equations with Boundary Conditions Polynomially Dependent on the Spectral Parameter

Guo

Wei

2014

Results. Math.

View full text Add to dashboard Cite

Inverse nodal problem for the Dirac operator on a finite interval with boundary conditions depending polynomially on the spectral parameter is considered. We prove that a set of nodal points of one of the components of the eigenfunctions uniquely determines the coefficients of the Dirac equations and the polynomials of the boundary conditions. Mathematics Subject Classification (2010). Primary 34L05, 34A55; Secondary 34L40.

show abstract

Solution of inverse nodal problems

Abstract: In this paper 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.

Cited by 162 publications

References 12 publications

Inverse problems: recovery of BV coefficients from nodes

Inverse problems: recovery of BV coefficients from nodes

Inverse nodal problem for p_Laplacian diffusion equation with polynomially dependent spectral parameter

Inverse Nodal Problem for Dirac Equations with Boundary Conditions Polynomially Dependent on the Spectral Parameter

Contact Info

Product

Resources

About