Search results for "Integral equations"
showing 10 items of 24 documents
Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations
2011
We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.
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.
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.
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.
CAD of complex passive devices composed of arbitrarily shaped waveguides using Nyström and BI-RME methods
2004
In this paper, a novel computer-aided design (CAD) tool of complex passive microwave devices in waveguide technology is proposed. Such a tool is based on a very efficient integral-equation analysis technique that provides a full-wave characterization of discontinuities between arbitrarily shaped waveguides defined by linear, circular, and/or elliptical arcs. For solving the modal analysis of such arbitrary waveguides, a modified version of the well-known boundary integral-resonant-mode expansion (BI-RME) method using the Nyström approach, instead of the traditional Galerkin version of the method of moments, is proposed, thus providing significant savings on computational costs and implement…
Efficient Analysis of Arbitrarily Shaped Inductive Obstacles in Rectangular Waveguides Using a Surface Integral Equation Formulation
2007
In this paper we propose to use the Surface Integral Equation technique for the analysis of arbitrarily shaped Hplane obstacles in rectangular waveguides, which can contain both metallic and/or dielectric objects. The Green functions are formulated using both spectral and spatial images series, whose convergence behavior has been improved through several acceleration techniques. Proceeding in this way, the convergence of the series is not attached to the employment of any particular basis or test function, thus consequently increasing the flexibility of the implemented technique. In order to test the accuracy and numerical efficiency of the proposed method, results for practical microwave c…
An adaptive method for Volterra–Fredholm integral equations on the half line
2009
AbstractIn this paper we develop a direct quadrature method for solving Volterra–Fredholm integral equations on an unbounded spatial domain. These problems, when related to some important physical and biological phenomena, are characterized by kernels that present variable peaks along space. The method we propose is adaptive in the sense that the number of spatial nodes of the quadrature formula varies with the position of the peaks. The convergence of the method is studied and its performances are illustrated by means of a few significative examples. The parallel algorithm which implements the method and its performances are described.
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.
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.
Spherical harmonic expansion of fundamental solutions and their derivatives for homogenous elliptic operators
2017
In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansions…