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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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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Academic Science JournalIn the present paper explores a reverse Cauchy problem for a heat transfer issue described by the Helmholtz and modified Helmholtz equation. Our goal is to identify an unknown defect within a simply connected bounded domain , given the Dirichlet data ...
shurouq hasan +2 more
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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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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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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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Mean Value Properties of Solutions to the Helmholtz and Modified Helmholtz Equations [PDF]
Journal of Mathematical Sciences, 2021 11 pages, no ...
Nikolay Kuznetsov
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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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Boundary value problems for modified Helmholtz equations and applications [PDF]
Boundary Value Problems, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Longfei Gu, Zunwei Fu
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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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