Related papers: The vibrating inhomogeneous string: a topic for a …
Years ago S. Weinberg suggested the "Quasi-Particle" method (Q-P) for iteratively solving an integral equation, based on an expansion in terms of sturmian functions that are eigenfunctions of the integral kernel. An improvement of this…
Highly oscillatory integrals of composite type arise in electronic engineering and their calculations is a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is…
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…
This study discusses a class of linear systems of fractional differential equations with non-constant coefficients, with a particular focus on problems exhibiting highly oscillatory and non-smooth behavior. We first establish the regularity…
We examine the validity of the kinetic description of wave turbulence for a model quadratic equation. We focus on the space-inhomogeneous case, which had not been treated earlier; the space-homogeneous case is a simple variant. We determine…
The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the…
The extension of the classical Bayesian penalized spline method to inference on vector-valued functions is considered, with an emphasis on characterizing the suitability of the method for general application.We show that the standard…
We develop a numerical method for computing with orthogonal polynomials that are orthogonal on multiple, disjoint intervals for which analytical formulae are currently unknown. Our approach exploits the Fokas--Its--Kitaev Riemann--Hilbert…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed: (1) motivated by an analogy with the Camassa-Holm equation a class of isospectral…
We study the small vibrations of axially moving strings described by a wave equation in an interval with two endpoints moving in the same direction with a constant speed. The solution is expressed by a series formula where the coefficients…
Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of…
We develop a spectral method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, the computational cost is reduced…
In this work we present a novel linear iterative solution to an electromagnetic inverse scattering problem with phaseless data for strongly scattering, lossy media. It is based on an extended Rytov approximation that significantly widens…
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
We introduce and analyse a sparse spectral method for the solution of Volterra integral equations using bivariate orthogonal polynomials on a triangle domain. The sparsity of the Volterra operator on a weighted Jacobi basis is used to…
We consider the solvability of the direct scattering problem of an obliquely incident time-harmonic electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. We prove the existence and uniqueness…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
A spectral method is considered for approximating the fractional Laplacian and solving the fractional Poisson problem in 2D and 3D unit balls. The method is based on the explicit formulation of the eigenfunctions and eigenvalues of the…
We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the…