Related papers: The vibrating inhomogeneous string: a topic for a …
The Levin method is a well-known technique for evaluating oscillatory integrals, which operates by solving a certain ordinary differential equation in order to construct an antiderivative of the integrand. It was long believed that this…
In this paper, we present the Stroboscopic Averaging Method (SAM), recently introduced in [7,8,10,12], which aims at numerically solving highly-oscillatory differential equations. More specifically, we first apply SAM to the Schr\"odinger…
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by…
We introduce new numerical integration operators which compose the mass and stiffness matrices of a modified spectral element method for simulation of elastic wave propagation. While these operators use the same quadrature nodes as does the…
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
We describe a method of solving the nuclear Skyrme-Hartree-Fock problem by using a deformed Cartesian harmonic oscillator basis. The complete list of expressions required to calculate local densities, total energy, and self-consistent…
In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper by A. Szij\'art\'o and J. Heged\H{u}s in which the authors ask the question of determining the initial data by only…
We study a fixed point iterative method based on generalized relaxation of strictly quasi-nonexpansive operators. The iterative method is assembled by averaging of strings, and each string is composed of finitely many strictly…
A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands…
By theoretical derivation, we constructed an inhomogeneous coefficient equation to correctly describing harmonic radiation in solids induced by a spatially inhomogeneous field, where the widely used semiconductor Bloch equation fails. This…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…
We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential…
In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
We study rigidly rotating and pulsating strings in the background of a 1+1 dimensional intersection of two orthogonal stacks of fivebranes in type IIB string theory by using the Neumann-Rosochatius (NR) model. Starting with the Polyakov…
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…
The time evolution of an oscillator coupled to an infinite string with a discontinuous mass density is investigated. It is shown that the equation of motion of the oscillator leads to a nonlinear characteristic equation due to the…
We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…