Solutions Of Convolution Equations Research Articles

A Method of Parametric Solution of Convolution Equations

A Method of Parametric Solution of Convolution Equations

On solutions of convolution equations in spaces of ultradifferentiable functions

On solutions of convolution equations in spaces of ultradifferentiable functions

FD2TD ANALYSIS OF ELECTROMAGNETIC FIELD PROPAGATION IN MULTIPOLE DEBYE MEDIA WITH AND WITHOUT CONVOLUTION

This paper deals with the time-domain numerical calculation of electromagnetic (EM) fields in linearly dispersive media described by multipole Debye model. The frequency-dependent finite-difference time-domain (FD2TD) method is applied to solve Debye equations using convolution integrals or by direct integration. Original formulations of FD2TD methods are proposed using different approaches. In the first approach based on the solution of convolution equations, the exponential analytical behavior of the convolution integrand permits an efficient recursive FD2TD solution. In the second approach, derived by circuit theory, the transient equations are directly solved in time domain by the FD2TD method. A comparative analysis of several FD2TD methods in terms of stability, dispersion, computational time and memory is carried out.

Representation of solutions of convolution equations in nonquasianalytic beurling classes of ultradifferentiable functions of mean type

We consider convolution equations in nonquasianalytic Beurling spaces of ultradifferentiable functions of mean type. We obtain a representation for a particular solution to such an equation as an exponential series whose coefficients are determined by the right-hand side of the equation.

A systematic derivation of Green's and Poisson's matrices for boundary-value problems in elastostatic half-spaces

Green's and Poisson's matrices in an n-dimensional half-space are computed for the system of linear isotropic elasticity and four types of boundary conditions attacked by Boussinesq and Cerruti by means of potential-theoretic methods and reconsidered by Sneddon (1993). This involves the solution of convolution equations and the computation of various convolution products by means of distribution theory. The question of uniqueness is also addressed.

Deconvolution with wavelets and vaguelettes

The use of wavelets for the solution of convolution equations is studied as a possible alternative to the well-established Fast Fourier Transform (FFT) technique. Two possible solution strategies are investigated: (1) The use of wavelets for the representation of both the given data and the unknown solution. This leads to an algorithm with good de-noising and data-compression properties. In terms of computational efficiency this algorithm is inferior to FFT. (2) The use of wavelets for the representation of the unknown solution and of so-called vaguelettes for the representations of the given data. This leads to an algorithm which is even faster than FFT.

Regularized Solutions of a Nonlinear Convolution Equation on the Euclidean Group

In this paper we apply Fourier analysis on the two and three dimensional Euclidean motion groups to the solution of a nonlinear convolution equation. First, we review the theory of the irreducible unitary representations of the motion group and discuss the corresponding Fourier transform of functions on the motion group. The main reasons why exact solutions of this convolution equation do not exist in many cases are discussed. Techniques for regularization of the problem and numerical methods for finding approximate solutions are presented. Examples are considered and approximate solutions are found.

Methods of factorization applicable to the solution of convolution equations

The aimj of this paper is to present methods of factorization applicable to the solution of convolution equations by means of Mikusinski's operational calculus. These methods are then applied for the solution of an evasion problem.

Solutions of Convolution Equations in Convex Sets

Solutions of Convolution Equations in Convex Sets

An economical method for the numerical solution of convolution equations

An economical method for the numerical solution of convolution equations