Results 21 to 30 of about 6,679 (246)
Modified Representations for the Close Evaluation Problem
Mathematical and Computational Applications, 2021 When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when ...
Camille Carvalho
doaj +1 more source
Mathematics, 2022 Inhomogeneous elliptical inclusions with partial differential equations have aroused appreciable concern in many disciplines. In this paper, a pseudo-spectral collocation method, based on Fourier basis functions, is proposed for the numerical solutions ...
Xiao Wang +3 more
doaj +1 more source
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 +1 more source
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
doaj +1 more source
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
doaj +1 more source
Exploring the Origin of Maximum Entropy States Relevant to Resonant Modes in Modern Chladni Plates
Entropy, 2022 The resonant modes generated from the modern Chladni experiment are systematically confirmed to intimately correspond to the maximum entropy states obtained from the inhomogeneous Helmholtz equation for the square and equilateral triangle plates.
Yu-Hsin Shu +5 more
doaj +1 more source
Mathematics, 2023 A piecewise-homogeneous medium, consisting of anisotropic layers, is excited by a primary spherical sound wave due to a point source lying in the exterior of the medium or in one of its layers.
Andreas Kalogeropoulos +1 more
doaj +1 more source
A Modified Natural BEM for Exterior Problems of the Helmholtz Equation [PDF]
Advances in Intelligent Systems Research, 2015 In this paper, a modified natural boundary element method (MNBEM) by using a modified DtN operator to improve the natural boundary element method (NBEM) is proposed for Neumann BVPs of the Helmholtz equation on unbounded domains. We prove the existence and the uniqueness of the solution of its variational problem in L 2 (Γ), and obtain L 2 error ...
Yue Gao, Quan Zheng
openaire +1 more source
Partial Differential Equations in Applied MathematicsThe modified Helmholtz equation qxx+qyy−4β2q=0, is one of the basic equations of classical mathematical physics. In this paper we have obtained the solution of the boundary-value problems for the modified Helmholtz equation in an equilateral triangle. An
Pratul Gadagkar +2 more
doaj +1 more source
The Solution of the modified Helmholtz equation in a wedge and an application to diffusion-limited coalescence [PDF]
Physics Letters A, 1999 The general solution of the modified Helmholtz equation, q_{xx}(x,y)+q_{yy}(x,y)-4b^2q(x,y)=0, in the wedge 0 < x < y < infinity, is presented. This solution is used to find the explicit steady-state of diffusion-limited coalescence, A+AA, on the half-line, with a trap-source at the origin.
ben-Avraham, Daniel +1 more
openaire +2 more sources