Related papers: Removing numerical dispersion from linear evolutio…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
The paper considers the application of two numerical models to simulate the evolution of steep breaking waves. The first one is a Lagrangian wave model based on equations of motion of an inviscid fluid in Lagrangian coordinates. A method…
Taylor's model of dispersion simply describes the long-term spread of material along a pipe, channel or river. However, often we need multi-mode models to resolve finer details in space and time. Here we construct zonal models of dispersion…
In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the…
Motivated by recent experiments, the theoretical study of wave propagation in time varying materials is of current interest. Although significant in nearly all such experiments, material dispersion is commonly neglected in theoretical…
We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…
In this paper, we consider the adaptive Eulerian--Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a…
In this article, we consider abstract linear conservative systems and their time-discrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the corresponding…
Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it's only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential…
Evolutionary computation techniques have mostly been used to solve various optimization and learning problems successfully. Evolutionary algorithm is more effective to gain optimal solution(s) to solve complex problems than traditional…
This article considers the use of total variation minimization for the recovery of a superposition of point sources from samples of its Fourier transform along radial lines. We present a numerical algorithm for the computation of solutions…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
Partial differential equations with highly oscillatory input terms are hardly ever solvable analytically and their numerical treatment is difficult. Modulated Fourier expansion used as an {\it ansatz} is a well known and extensively…
We introduce and analyze a class of Galerkin-collocation discretization schemes in time for the wave equation. Its conceptual basis is the establishment of a direct connection between the Galerkin method for the time discretization and the…
This paper introduces weighted finite difference methods for numerically solving dispersive evolution equations with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled cubic nonlinear…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
Particle-mesh simulations trade small-scale accuracy for speed compared to traditional, computationally expensive N-body codes in cosmological simulations. In this work, we show how a data-driven model could be used to learn an effective…
Electrostatic correlations and fluctuations in ionic systems can be described within an extended Poisson-Boltzmann theory using a Gaussian variational form. The resulting equations are challenging to solve because they require the solution…