Results 1 to 10 of about 63,372 (284)
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
doaj +5 more sources
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
doaj +3 more sources
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
doaj +3 more sources
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
doaj +4 more sources
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
doaj +2 more sources
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
doaj +2 more sources
Fast integral equation methods for the modified Helmholtz equation [PDF]
Journal of Computational Physics, 2011 Many problems in physics and engineering require the solution of the forced heat equation, $u_{t}-Delta u = F(xx,u,t)$, with Dirichlet boundary conditions. In this thesis, we solve such PDEs in two-dimensional, multiply-connected domains, with a twice continuously differentiable boundary.
Kropinski, Mary Catherine A. +1 more
openaire +5 more sources
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
doaj +1 more source
Mean Value Properties of Solutions to the Helmholtz and Modified Helmholtz Equations [PDF]
Journal of Mathematical Sciences, 2021 11 pages, no ...
openaire +2 more sources
PENENTUAN JENIS FUNGSI BASIS RADIAL DALAM DUAL RECIPROCITY BOUNDARY ELEMENT METHOD
Majalah Ilmiah Matematika dan Statistika, 2021 Problems involving modified Helmholtz equation are considered in this paper. To solve the problem numerically, dual reciprocity boundary element method (DRBEM) is employed.
Millatuz Zahroh
doaj +1 more source