Search results for " integral equations."
showing 10 items of 18 documents
Alternative boundary integral equations for fracture mechanics in 2D anisotropic bodies
2017
An alternative dual boundary element formulation for generally anisotropic linear elastic twodimensional bodies is presented in this contribution. The formulation is based on the decomposition of the displacement field into the sum of a vector field satisfying the anisotropic Laplace equation and the gradient of the classic Airy stress function. By suitable manipulation of the integral representation of the anisotropic Laplace equation, a set of alternative integral equations is obtained, which can be used in combination with the displacement boundary integral equation for the solution of crack problems. Such boundary integral equations have the advantage of avoiding hyper-singular integral…
Wavelet-like bases for thin-wire integral equations in electromagnetics
2005
AbstractIn this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis trans…
A nonstandard Volterra integral equation on time scales
2019
Abstract This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.
Efficient analysis of waveguide filters by the integral equation technique and the BI-RME method
2003
This paper presents the study of rectangular waveguide filters with rounded corners in the cross-section of the waveguides. These components are suitable for low-cost mass production and can be rigorously analyzed by efficient CAD tools. The analysis approach described in this paper is based on the integral equation technique in conjunction with the boundary integral-resonant mode expansion method. Two representative examples are also reported.
Common fixed point results on quasi-Banach spaces and integral equations
2013
In this paper we obtain fixed and common fixed point theorems for self-mappings defined on a closed and convex subset C of a quasi-Banach space. We give also a constructive method for finding the common fixed points of the involved mappings. As an application we obtain a result of the existence of solutions of integral equations.
Multi-parameter analysis of the obstacle scattering problem
2022
Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.
Shapes of a gas bubble rising in the vertical Hele–Shaw cell with magnetic liquid
2005
Abstract Dynamics of the bubble rising in the vertical Hele–Shaw cell with magnetic liquid in the normal magnetic field is studied. Linear stability analysis of the circular shape is carried out. Development of the instability with respect to the lowest symmetric mode is simulated by the boundary integral equation technique.
A note on the uniqueness and attractive behavior of solutions for nonlinear Volterra equations
2001
In this paper we prove that positive solutions of some nonlinear Volterra integral equations must be locally bounded and global attractors of positive functions. These results complete previous results about the existence and uniqueness of solutions and their attractive behavior.
Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness
2012
Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.
Quadrature rules for qualocation
2003
Qualocation is a method for the numerical treatment of boundary integral equations on smooth curves which was developed by Chandler, Sloan and Wendland (1988-2000) [1,2]. They showed that the method needs symmetric J–point–quadrature rules on [0, 1] that are exact for a maximum number of 1–periodic functions The existence of 2–point–rules of that type was proven by Chandler and Sloan. For J ∈ {3, 4} such formulas have been calculated numerically in [2]. We show that the functions Gα form a Chebyshev–system on [0, 1/2] for arbitrary indices a and thus prove the existence of such quadrature rules for any J.