相关论文: A new discrete energy technique for multi-step bac…

We propose a novel, highly efficient, mean-reverting-SAV-BDF2-based, long-time unconditionally stable numerical scheme for a class of finite-dimensional nonlinear models important in geophysical fluid dynamics. The scheme is highly…

Ensuring the safe and reliable operation of integrated electricity and gas systems (IEGS) requires dynamic energy flow (DEF) simulation tools that achieve high accuracy and computational efficiency. However, the inherent strong nonlinearity…

A second order accurate numerical scheme is proposed and analyzed for the periodic three-component Macromolecular Microsphere Composite(MMC) hydrogels system, a ternary Cahn-Hilliard system with a Flory-Huggins-deGennes free energy…

We study a discrete-time approximation for solutions of systems of decoupled forward-backward doubly stochastic differential equations (FBDSDEs). Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the…

We use backward error analysis for differential equations to obtain modified or distorted equations describing the behaviour of the Newmark scheme applied to the transient structural dynamics equation. Based on the newly derived distorted…

The Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation is a classical reaction-diffusion equation with broad applications such as biology, chemistry and physics. In this paper, an alternative second-order scheme is proposed by employing a…

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…

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…

The present study aims at further development of covariant energy density functionals (CEDFs) towards more accurate description of binding energies across the nuclear chart. For the first time, infinite basis corrections to binding energies…

Motivated by the idea of imposing paralleling computing on solving stochastic differential equations (SDEs), we introduce a new Domain Decomposition Scheme to solve forward-backward stochastic differential equations (FBSDEs) parallely. We…

In this paper, we propose a family of time-stepping schemes for approximating general nonlinear Schr\"odinger equations. The proposed schemes all satisfy both mass conservation and energy conservation. Truncation and dispersion error…

In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative…

We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic calculations. We consider a model one-dimensional partial…

We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of…

Recent advances in neural-network architecture allow for seamless integration of convex optimization problems as differentiable layers in an end-to-end trainable neural network. Integrating medium and large scale quadratic programs into a…

A second-order backward differentiation formula (BDF2) finite-volume discretization for a nonlinear cross-diffusion system arising in population dynamics is studied. The numerical scheme preserves the Rao entropy structure and conserves the…

We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to…

We develop a spectrally accurate numerical method to compute solutions of a model partial differential equation used in plasma physics to describe diffusion in velocity space due to Fokker-Planck collisions. The solution is represented as a…

The existing discrete variational derivative method is only second-order accurate and fully implicit. In this paper, we propose a framework to construct an arbitrary high-order implicit (original) energy stable scheme and a second-order…

A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…