Coefficient identification in Euler–Bernoulli equation from over-posed data

Marinov, Tchavdar; Marinova, Rossitza S.

doi:10.1016/j.cam.2010.05.048

Cited by 15 publications

(15 citation statements)

References 8 publications

(11 reference statements)

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“…Now we use the equality (12) on the right-hand side of formula (10) to obtain the first variation of the cost functional ( ). Then we have…”

Section: Frechet Differentiability Of the Cost Functionalmentioning

confidence: 99%

“…In [5], Papanicolau solved the problem of determining of the flexural rigidity coefficient ( ) in the equation ( ( ) ( )) ( ) ( ) , where ( ) is the deflection of the beam. Inverse coefficient identification problems governed by the steady state Euler-Bernoulli beam equation are studied in [6][7][8][9][10].…”

Section: Introduction and Optimal Control Problem Formulationmentioning

confidence: 99%

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Identification of the Transverse Distributed Load in the Euler-Bernoulli Beam Equation from Boundary Measurement

Saraç¹,

Şener²

2018

IJMO

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Abstract-This paper is concerned with an optimal control problem for the Euler-Bernoulli beam equation. We assume that the transverse distributed load is a control function. We prove the existence of the unique optimal solution in the suitable set of admissible control. We get the gradient of the cost functional by using the adjoint problem.Index Terms-Euler-Bernoulli beam equation, optimization, boundary measurement, frechet differentiability.

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“…Now we use the equality (12) on the right-hand side of formula (10) to obtain the first variation of the cost functional ( ). Then we have…”

Section: Frechet Differentiability Of the Cost Functionalmentioning

confidence: 99%

Section: Introduction and Optimal Control Problem Formulationmentioning

confidence: 99%

Identification of the Transverse Distributed Load in the Euler-Bernoulli Beam Equation from Boundary Measurement

Saraç¹,

Şener²

2018

IJMO

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“…The Method of Variational Imbedding (MVI) is used for solving the inverse problem (see for example [8,9], and [6] in case of elliptic PDE's).…”

Section: Variational Imbeddingmentioning

confidence: 99%

“…This fact allows us to consider the problem on the half-line(see Figure 1). Then the boundary conditions for x = 0 reads: www.arjonline.org 35 (8) under boundary conditions…”

Section: Introducing Unknown Coefficientmentioning

confidence: 99%

Numerical Identification of Solitary Wave-Like solutions in Boussinesq Equation as Inverse Problem

2015

American Research Journal of Mathematics

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An algorithm to investigate numerically the solitary wave-like solutionsof Boussinesq differential equation is constructed. The bifurcation problem is re-formulated as an inverse problem for coefficient identification, introducing a newparameter. Such a way the nontrivial solution is separated from the trivial one.The Method of Variational Imbedding (MVI) is used for solving the inverse prob-lem. As illustration of the approach a Mathematica code with the finite differencescheme is prepared and the numerical results, including verification of the scheme,connection between the solution and the coefficients, and capability of Mathematica to paralelize the algorithm are presented.

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“…(see for example [1] and [2]). In those cases the Fundamental Theorem of Calculus cannot be applied and the values of the integral have to be approximated numerically.…”

Section: Introductionmentioning

confidence: 99%

Behavior of the Numerical Integration Error

Marinov

Omojola²,

Washington³

et al. 2014

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In this work, we consider different numerical methods for the approximation of definite integrals. The three basic methods used here are the Midpoint, the Trapezoidal, and Simpson's rules. We trace the behavior of the error when we refine the mesh and show that Richardson's extrapolation improves the rate of convergence of the basic methods when the integrands are sufficiently differentiable many times. However, Richardson's extrapolation does not work when we approximate improper integrals or even proper integrals from functions without smooth derivatives. In order to save computational resources, we construct an adaptive recursive procedure. We also show that there is a lower limit to the error during computations with floating point arithmetic.

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Coefficient identification in Euler–Bernoulli equation from over-posed data

Cited by 15 publications

References 8 publications

Identification of the Transverse Distributed Load in the Euler-Bernoulli Beam Equation from Boundary Measurement

Identification of the Transverse Distributed Load in the Euler-Bernoulli Beam Equation from Boundary Measurement

Numerical Identification of Solitary Wave-Like solutions in Boussinesq Equation as Inverse Problem

Behavior of the Numerical Integration Error

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