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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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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Modified Finite Difference Schemes on Uniform Grids for Simulations of the Helmholtz Equation at Any Wave Number [PDF]
Journal of Applied Mathematics, 2014 We construct modified forward, backward, and central finite difference schemes, specifically for the Helmholtz equation, by using the Bloch wave property.
Hafiz Abdul Wajid +3 more
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Generalized Tikhonov Method and Convergence Estimate for the Cauchy Problem of Modified Helmholtz Equation with Nonhomogeneous Dirichlet and Neumann Datum [PDF]
Mathematics, 2019 We investigate a Cauchy problem of the modified Helmholtz equation with nonhomogeneous Dirichlet and Neumann datum, this problem is ill-posed and some regularization techniques are required to stabilize numerical computation. We established the result of
Hongwu Zhang, Xiaoju Zhang
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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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A G-Modified Helmholtz Equation with New Expansions for the Earth’s Disturbing Gravitational Potential, Its Functionals and the Study of Isogravitational Surfaces [PDF]
AppliedMathThe G-modified Helmholtz equation is a partial differential equation that enables us to express gravity intensity g as a series of spherical harmonics having radial distance r in irrational powers.
Gerassimos Manoussakis
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Nodally exact Ritz discretizations of 1D diffusion–absorption and Helmholtz equations by variational FIC and modified equation methods [PDF]
, 2007 The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-005-0011-zThis article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework.
Felippa, Carlos +1 more
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Academic Science JournalIn this study, a heat conduction in fin-related inverse problem for the modified Helmholtz equation is taken into consideration. The purpose of this study is to estimate the temperature on an under-specified boundary (a part of the outer border of a ...
shaimaa aamer, Fatima M. Aboud
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A Regularization Method to Solve a Cauchy Problem for the Two-Dimensional Modified Helmholtz Equation [PDF]
Mathematics, 2019 In this paper, the ill-posed problem of the two-dimensional modified Helmholtz equation is investigated in a strip domain. For obtaining a stable numerical approximation solution, a mollification regularization method with the de la Vallée Poussin ...
Shangqin He, Xiufang Feng
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Numerical Study on Oil Particle Enrichment in a Rectangular Microfluidic Channel Based on Acoustic Standing Waves [PDF]
MicromachinesThis study presents a method for enriching oil-suspended particles within a rectangular microfluidic channel using acoustic standing waves. A modified Helmholtz equation is solved to establish the acoustic field model, and the equilibrium between ...
Zhenzhen Liu +5 more
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