相关论文: A novel second-order nonstandard finite difference…

We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…

We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…

In this work, neutral stochastic functional differential equations with infinite delay (NSFDEwID) has been studied. The existence and uniqueness of solutions to NSFDEwID at the state space $ C_{r} $ under the local weak monotone condition,…

Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…

This paper is concerned with developing accurate and efficient numerical methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in multiple spatial dimensions. It presents a general framework…

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…

When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. In this work, we propose…

Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local…

In this paper, an efficient algorithm is presented by the extrapolation technique to improve the accuracy of finite difference schemes for solving the fractional boundary value problems with non-smooth solution. Two popular finite…

In this paper, we consider the finite difference method for the generalized two-dimensional (2D) multi-term time-fractional Oldroyd-B fluid model, which is a subclass of non-Newtonian fluids. Different from the general multi-term time…

In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…

We describe a family of descent algorithms which generalizes common existing schemes used in applications such as neural network training and more broadly for optimization of smooth functions--potentially for global optimization, or as a…

We present an energy/entropy stable and high order accurate finite difference (FD) method for solving the nonlinear (rotating) shallow water equations (SWEs) in vector invariant form using the newly developed dual-pairing and…

We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…

We propose a systemic method of applying the auxiliary systems of original equations to find the high order nonlocal symmetries of nonlinear evolution equation. In order to validate the effectiveness of the method, some examples are…

This paper presents an adaptive hyperviscosity stabilisation procedure for the Radial Basis Function-generated Finite Difference (RBF-FD) method, aimed at solving linear and non-linear advection-dominated transport equations on domains…

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the…

NVIDIA researchers have pioneered an explicit method, position-based dynamics (PBD), for simulating systems with contact forces, gaining widespread use in computer graphics and animation. While the method yields visually compelling…