Related papers: Development of accurate solutions for a classical …
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
A generalized equation is constructed for a class of classical oscillators with strong anharmonicity which are not exactly solvable. Aboodh transform based homotopy perturbation method (ATHPM) is applied to get the approximate analytical…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
We propose an operational method for the solution of differential equations involving vector products. The technique we propose is based on the use of the evolution operator, defined in such a way that the wealth of techniques developed…
We study the dynamics of an infinite regular lattice of classical charged oscillators. Each individual oscillator is described as a point particle subject to a harmonic restoring potential, to the retarded electromagnetic field generated by…
We propose a new analytical method to solve for the nonexactly solvable Schrodinger equation. Successfully, it is applied to a class of spiked harmonic oscillators and truncated Coulomb potentials. The utility of this method could be…
A new method for solving non-autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
Composite optimization problems, where the sum of a smooth and a merely lower semicontinuous function has to be minimized, are often tackled numerically by means of proximal gradient methods as soon as the lower semicontinuous part of the…
A systematic method for calculating higher-order corrections of the relativistic semiclassical fixed-energy amplitude is given. The central scheme in computing corrections of all orders is related to a time ordering operation of an operator…
We present the consistent approach to finding the discrete transformations in the representation spaces of the proper Poincar\'e group. To this end we use the possibility to establish a correspondence between involutory automorphisms of the…
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
We present various exact solutions of a discrete complex Ginzburg-Landau (CGL) equation on a plane lattice, which describe target patterns and spiral patterns and derive their stability criteria. We also obtain similar solutions to a system…
The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…
The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…
We consider the conformal wave equation on the Einstein cylinder with a defocusing cubic non-linearity. Motivated by a method developed by Rostworowski-Maliborski on the existence of time periodic solutions to the spherically symmetric…
A classic harmonic oscillator model is developed to investigate the optical properties of coupled metal nanoparticles (MNPs) with arbitrary configuration in plane. The coupling coefficients are derived from classical electrodynamics. Using…
A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of…
In the article we lead a brief survey of contemporary gradient type methods (with inexact oracle) for stochastic optimization problems.