Fourier Truncation Regularization Method for a Three-Dimensional Cauchy Problem of the Modified Helmholtz Equation with Perturbed Wave Number [PDF]
Mathematics, 2019 In this paper, the Cauchy problem of the modified Helmholtz equation (CPMHE) with perturbed wave number is considered. In the sense of Hadamard, this problem is severely ill-posed. The Fourier truncation regularization method is used to solve this Cauchy
Fan Yang, Ping Fan, Xiao-Xiao Li
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On Solving Modified Helmholtz Equation in Layered Materials Using the Multiple Source Meshfree Approach [PDF]
Mathematics, 2019 This paper presents a study for solving the modified Helmholtz equation in layered materials using the multiple source meshfree approach (MSMA). The key idea of the MSMA starts with the method of fundamental solutions (MFS) as well as the collocation ...
Cheng-Yu Ku +3 more
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A New Modified Helmholtz Equation for the Expression of the Gravity Gradient and the Intensity of an Electrostatic Field in Spherical Harmonics [PDF]
Mathematics, 2023 In this work, it is shown that the geometry of a gravity field generated by a spheroid with low eccentricity can be described with the help of a newly modified Helmholtz equation.
Gerassimos Manoussakis
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Solution to the Modified Helmholtz Equation for Arbitrary Periodic Charge Densities [PDF]
Frontiers in Physics, 2021 We present a general method for solving the modified Helmholtz equation without shape approximation for an arbitrary periodic charge distribution, whose solution is known as the Yukawa potential or the screened Coulomb potential.
Miriam Winkelmann +13 more
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Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method [PDF]
Journal of Mathematics, 2022 The Quasi-Reversibility Regularization Method (Q-RRM) provides stable approximate solution of the Cauchy problem of the Helmholtz equation in the Hilbert space by providing either additional information in the Laplace-type operator in the Helmholtz ...
Benedict Barnes +3 more
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Characterization of balls via solutions of the modified Helmholtz equation [PDF]
Comptes Rendus. Mathématique, 2021 A theorem characterizing analytically balls in the Euclidean space $\mathbb{R}^m$ is proved. For this purpose positive solutions of the modified Helmholtz equation are used instead of harmonic functions applied in previous results.
Kuznetsov, Nikolay
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The Quasireversibility Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation [PDF]
Journal of Applied Mathematics, 2013 This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data ...
Xiao-Xiao Li +3 more
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Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation [PDF]
Complexity, 2020 In this paper, we derive the convergence for the high-accuracy algorithm in solving the Dirichlet problem of the modified Helmholtz equation. By the boundary element method, we transform the system to be a boundary integral equation.
Hu Li, Guang Zeng
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A quasi-reversibility regularization method for a Cauchy problem of the modified Helmholtz-type equation [PDF]
Boundary Value Problems, 2019 The Cauchy problem of the modified Helmholtz-type equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Thus the regularization methods are required to recover the numerical stability. In this paper, we
Hong Yang, Yanqi Yang
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Polynomial Approximation of an Inverse Cauchy Problem for Modified Helmholtz Equations
Academic Science Journal, 2023 In this paper, an inverse problem for the modified Helmholtz equation arising in heat conduction in the fin is considered. The goal of this paper is the determination of the temperature at the under-specified boundary (inner boundary of an annular domain)
Athraa Falih Hasanl +4 more
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