相关论文: Higher-order error estimates of the discrete-time …

We propose a $k^{\rm th}$-order unfitted finite element method ($2\le k\le 4$) to solve the moving interface problem of the Oseen equations. Thorough error estimates for the discrete solutions are presented by considering errors from…

This work constructs and analyzes new efficient high-order two-derivative diagonally implicit Runge--Kutta (TDDIRK) schemes with optimized phase errors. Specifically, we present a convergence result for TDDIRK methods and investigate their…

In recent years, higher-order trace formulas of operator functions have attracted considerable attention to a large part of the perturbation theory community. In this direction, we prove estimates for traces of higher-order derivatives of…

It is well known that both gradient descent and stochastic coordinate descent achieve a global convergence rate of $O(1/k)$ in the objective value, when applied to a scheme for minimizing a Lipschitz-continuously differentiable,…

This is the second part of study on the optimal convergence rate of the explicit Euler discretization in time for the convection-diffusion equations [Appl. Math. Lett. \textbf{131} (2022) 108048] which focuses on high-dimensional…

We calculate, for the first time, the next-to-next-to leading order (NNLO) QCD corrections to spin correlations in top quark pair production at the LHC. The NNLO corrections play an important role in the description of the corresponding…

Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…

This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…

In the present paper, a discrete version of It\^o's formula for a class of multi-dimensional random walk is introduced and applied to the study of a discrete-time complete market model which we call He's framework. The formula unifies…

We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.

The discrete gradient structure and the positive definiteness of discrete fractional integrals or derivatives are fundamental to the numerical stability in long-time simulation of nonlinear integro-differential models. We build up a…

A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…

In 1986, Dixon and McKee developed a discrete fractional Gr\"{o}nwall inequality [Z. Angew. Math. Mech., 66 (1986), pp. 535--544], which can be seen as a generalization of the classical discrete Gr\"{o}nwall inequality. However, this…

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step…

We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in [Wu,…

Recently, the high-resolution ordinary differential equation (ODE) framework, which retains higher-order terms, has been proposed to analyze gradient-based optimization algorithms. Through this framework, the term $\nabla^2…

The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive…

In [8] (Nakagawa, et.al., IEEE Trans. IT, 2021), we investigated the convergence speed of the Arimoto-Blahut algorithm. In [8], the convergence of the order $O(1/N)$ was analyzed by focusing on the second-order nonlinear recurrence formula…

The computation of perturbative corrections to processes involving heavy quarks is crucial for the precision program of the LHC and future colliders. In this article, we describe a powerful approach to calculate higher-orders in QCD…

In this paper, we consider the higher-order linear Schr\"odinger equations, that is, a formal finite Taylor expansion of the linear pseudo-relativistic equation. We establish the global-in-time Strichartz estimates for these higher-order…