Applications of finite and infinite Fourier series in heat processes with impulse data

Faydaoğlu, Şerife; Yakhno, V. G.

doi:10.1016/j.amc.2011.08.093

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Fourth-order Linear Differential Equations With Impulse1

Introduction1

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Cited by 3 publications

(2 citation statements)

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“…Notice that it follows that W 0 (θ , φ ) = αβ γδW b (ϕ, ψ), [4]. Now, we introduce the Green function if W b (ϕ, ψ) = 0, then the nonhomogeneous BVPI (12), (8), (9) has a unique solution y(x) for which the formula [2] …”

Section: Fourth-order Linear Differential Equations With Impulsementioning

confidence: 99%

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On spectral properties of a fourth-order boundary value problem with impulse

Faydaoğlu¹

2015

AIP Conference Proceedings

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In this paper, we consider a fourth-order boundary value problem with impulse. We apply the Fourier method for solving of this problem arising in finding of transverse vibration of a string. We calculate the eigenvalues and eigenfunctions of the fourth-order boundary value problem for some ordinary differential equation with piecewise constant coefficient. We obtain a solution of the considered equation subject to initial data, boundary and transmission conditions at the point of discontinuity.

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Section: Fourth-order Linear Differential Equations With Impulsementioning

confidence: 99%

“…The Fourier method for the partial differential equations with constants coefficient is a powerful tool [1][2][3][4][5]7]. But for the partial differential equation with piecewise constant coefficients this method is not developed much.…”

Section: Introductionmentioning

confidence: 99%