Results 11 to 20 of about 6,984 (280)
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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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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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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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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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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The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation [PDF]
Mathematical Problems in Engineering, 2011 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. The regularization solution is obtained by the simplified Tikhonov regularization method.
Yang, Fan, Guo, Hengzhen, Li, Xiaoxiao
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Boundary Value Problems, 2017 In this paper, we consider the inverse problem of identifying the unknown source for the modified Helmholtz equation. We propose the Landweber iterative regularization method to solve this problem and obtain the regularization solution.
Fan Yang, Xiao Liu, Xiao-Xiao Li
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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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The Convexity of a Planar Domain Via Properties of Solutions to the Modified Helmholtz Equation
Journal of Mathematical SciencesA new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan's formula, expressing the distance function with respect to the domain's boundary via real-valued solutions of the modified Helmholtz equation, and the convexity of a planar domain in which the distance function is ...
Kuznetsov, Nikolay
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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 ...
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