相关论文: A comparison of boundary correction methods for St…

We perform the analysis of the focusing nonlinear Schr\"odinger equation on the half-line with time-dependent boundary conditions along the lines of the nonlinear method of images with the help of B\"acklund transformations. The difficulty…

Distributed optimization aims to leverage the local computation and communication capabilities of each agent to achieve a desired global objective. This paper addresses the distributed pose graph optimization (PGO) problem under non-convex…

We present modifications of the second-order Douglas stabilizing corrections method, which is a splitting method based on the implicit trapezoidal rule. Inclusion of an explicit term in a forward Euler way is straightforward, but this will…

We extend the divergence preserving cut finite element method presented in [T. Frachon, P. Hansbo, E. Nilsson, S. Zahedi, SIAM J. Sci. Comput., 46 (2024)] for the Darcy interface problem to unfitted outer boundaries. We impose essential…

This review article aims to stress and reunite some of the analytic formalism of the anomalous diffusive processes that have succeeded in their description. Also, it has the objective to discuss which of the new directions they have taken…

We develop a unified framework for the design and analysis of high-order nonconforming virtual element methods for nonlinear fourth-order reaction--diffusion problems in two dimensions, with emphasis on clamped, Navier, and…

Since their introduction in 1967, Lawson methods have achieved constant interest in the time discretization of evolution equations. The methods were originally devised for the numerical solution of stiff differential equations. Meanwhile,…

In this paper we present a simple partitioning based technique to refine the statistical analysis of classification algorithms. The core of our idea is to divide the input space into two parts such that the first part contains a suitable…

In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…

We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $\ell$ in an infinite heterogeneous medium, in a situation where the medium is only known in a box of…

Numerical mode matching (NMM) methods are widely used for analyzing wave propagation and scattering in structures that are piece-wise uniform along one spatial direction. For open structures that are unbounded in transverse directions…

This article is devoted to the construction of new numerical methods for the semiclassical Schr\"odinger equation. A phase-amplitude reformulation of the equation is described where the Planck constant epsilon is not a singular parameter.…

We extend to the N-level Bloch model the splitting scheme which use exact numerical solutions of sub-equations. These exact solutions involve matrix exponentials which we want to avoid to calculate at each time step. We use Newton…

An efficient method is proposed for numerical solutions of nonlinear Schr\"{o}dinger equations in an unbounded domain. Through approximating the kinetic energy term by a one-way equation and uniting it with the potential energy equation,…

A new local discontinuous Galerkin (LDG) method for convection-diffusion equations on overlapping meshes with periodic boundary conditions was introduced in \cite{Overlap1}. With the new method, the primary variable $u$ and the auxiliary…

We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic…

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our…

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…

In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…