相关论文: An ADI extrapolated Crank-Nicolson orthogonal spli…

We prove the optimal strong convergence rate of a fully discrete scheme, based on a splitting approach, for a stochastic nonlinear Schr\"odinger (NLS) equation. The main novelty of our method lies on the uniform a priori estimate and…

We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schr\"odinger-Poisson system. More specifically, we use the Crank-Nicolson scheme as a time stepping mechanism, whilst…

We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a…

The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…

A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…

In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…

We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…

Chromatic dispersion is a common problem to degrade the system resolution in optical coherence tomography (OCT). This study is to develop a deep learning network for automated dispersion compensation (ADC-Net) in OCT. The ADC-Net is based…

Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…

This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…

Nonlocal diffusion model provides an appropriate description of the diffusion process of solute in the complex medium, which cannot be described properly by classical theory of PDE. However, the operators in the nonlocal diffusion models…

In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equation. To begin with, we construct an implicit difference…

We consider distributed optimization on undirected connected graphs. We propose a novel distributed conditional gradient method with (O(1/\sqrt{k})) convergence. Compared with existing methods, each iteration of our method uses both…

In this paper, we propose high-order numerical methods for the Riesz space fractional advection-dispersion equations (RSFADE) on a {f}inite domain. The RSFADE is obtained from the standard advection-dispersion equation by replacing the…

In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…

Early detection of anomalies in medical images such as brain MRI is highly relevant for diagnosis and treatment of many conditions. Supervised machine learning methods are limited to a small number of pathologies where there is good…

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…

We review our recently developed electronic structure calculation methods used for the dynamics of large-scale solids or liquids with an efficient algorithm for large scale simultaneous linear equations. The electronic structure calculation…

We provide a computational method for quickly determining the correct distribution of optically active nanoparticles for a desired response. This is achieved by simulating the optical response of single nanoparticles and performing a…