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The Modified Helmholtz Equation on a Regular Hexagon—The Symmetric Dirichlet Problem [PDF]
Axioms, 2020 Using the unified transform, also known as the Fokas method, we analyse the modified Helmholtz equation in the regular hexagon with symmetric Dirichlet boundary conditions; namely, the boundary value problem where the trace of the solution is given by ...
Konstantinos Kalimeris +1 more
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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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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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A Spectral Regularization Method for a Cauchy Problem of the Modified Helmholtz Equation [PDF]
Boundary Value Problems, 2010 We consider the Cauchy problem for a modified Helmholtz equation, where the Cauchy data is given at x=1 and the solution is sought in the interval 0<x<1.
Ailin Qian, Jianfeng Mao, Lianghua Liu
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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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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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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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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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Fast integral equation methods for the modified Helmholtz equation [PDF]
Journal of Computational Physics, 2011 Published in Computers & Mathematics with ...
Mary Catherine A. Kropinski +1 more
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Modified regularization method for the Cauchy problem of the Helmholtz equation
Applied Mathematical Modelling, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ting Wei
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