Related papers: Convergence of numerical schemes for short wave lo…
We study the global existence of small data solutions for Cauchy problem for the semi-linear structural damped wave equation with source term.
Gravitational waves provide a powerful enhancement to our understanding of fundamental physics. To make the most of their detection we need to accurately model the entire process of their emission and propagation toward interferometers.…
We report on a number of careful numerical experiments motivated by the semiclassical (zero-dispersion, \epsilon\downarrow 0) limit of the focusing nonlinear Schr\"odinger equation. Our experiments are designed to study the evolution of a…
We propose an efficient numerical scheme for the resolution of a non-hydrostatic Saint-Venant type model. The model is a shallow water type approximation of the incompressbile Euler system with free surface and slightly differs from the…
In this paper, we study both convergence and bounded variation properties of a new fully discrete conservative Lagrangian--Eulerian scheme to the entropy solution in the sense of Kruzhkov (scalar case) by using a weak asymptotic analysis.…
This work considers numerical methods for the time-dependent Schr\"{o}dinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensurate problem is lifted to a higher dimension that…
We develop a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. In order to numerically reproduce the blow-up phenomena, we propose a rule of scaling…
A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
The fractional discrete nonlinear Schr\"odinger equation (fDNLS) is studied on a periodic lattice from the analytic and dynamic perspective by varying the mesh size $h>0$ and the nonlocal L\'evy index $\alpha \in (0,2]$. We show that the…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
We establish the convergence of an approximation scheme to a model for aurora type phenomena. The latter, mathematically, means a system describing the short wave-long wave (SW-LW) interactions for compressible magnetohydrodynamic (MHD)…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
In this paper, we establish a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime. We combine the energy and pointwise decay results for solutions obtained in \cite{Yang} with a Sobolev embedding…
We prove strong convergence of a semi-discrete finite difference method for the KdV and modified KdV equations. We extend existing results to non-smooth data (namely, in $L^2$), without size restrictions. Our approach uses a fourth order…
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
We propose and analyze a structure-preserving approximation of the non-isothermal Cahn-Hilliard equation using conforming finite elements for the spatial discretization and a problem-specific mixed explicit-implicit approach for the…
We propose a new entropy-compatible neural network method for scalar hyperbolic conservation laws and establish, to our knowledge, the first explicit \(L^1\) convergence rates in this setting that apply to piecewise smooth entropy…
For the first time, Schr\"odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such…
This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…