Explanipedia

A new class of one-step A-stable and L-stable schemes of high-order accuracy for parabolic type equations Open

Xiaoyi Li, Aijie Cheng, Zhengguang Liu · 2025

Recently, a new class of BDF schemes proposed in [F. Huang and J. Shen, SIAM J Numer. Anal., 62.4, 1609--1637] for the parabolic type equations are studied in this paper. The basic idea is based on the Taylor expansions at time $t^{n+β}$ w…

A Fast Finite Difference Method for 2D Time Fractional Mobile/Immobile Equation with Weakly Singular Solution Open

Haili Qiao, Aijie Cheng · 2025

This paper presents a fast Crank–Nicolson L1 finite difference scheme for the two-dimensional time fractional mobile/immobile diffusion equation with weakly singular solution at the initial moment. First, the time fractional derivative is …

Improving the Transient Stability of a Stochastic Power System – Algorithms and Mathematical Analysis Open

Zhen Wang, Kaihua Xi, Aijie Cheng, Hai Xiang Lin, Jan H. van Schuppen · 2025

Improving the accuracy and consistency of the energy quadratization method with an energy-optimized technique Open

Xiaoqing Meng, Aijie Cheng, Zhengguang Liu · 2024

We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition t…

Optimal Control of a Stochastic Power System -- Algorithms and Mathematical Analysis Open

Zhen Wang, Kaihua Xi, Aijie Cheng, Hai Xiang Lin, Jan H. van Schuppen · 2024

The considered optimal control problem of a stochastic power system, is to select the set of power supply vectors which infimizes the probability that the phase-angle differences of any power flow of the network, endangers the transient st…

Control of the Power Flows of a Stochastic Power System Open

Zhen Wang, Kaihua Xi, Aijie Cheng, Hai Xiang Lin, Jan H. van Schuppen · 2023

How to determine the vector of power supplies of a stochastic power system for the next short horizon, such that the probability is less than a prespecified value that any phase-angle difference of a power line of the power network exits f…

A Critical Escape Probability Formulation for Enhancing the Transient Stability of Power Systems with System Parameter Design Open

Xian Wu, Kaihua Xi, Aijie Cheng, Chenghui Zhang, Hai Xiang Lin · 2023

For the enhancement of the transient stability of power systems, the key is to define a quantitative optimization formulation with system parameters as decision variables. In this paper, we model the disturbances by Gaussian noise and defi…

The high-order exponential semi-implicit scalar auxiliary variable approach for nonlocal Cahn-Hilliard equation Open

Xiaoqing Meng, Aijie Cheng, Zhengguang Liu · 2023

The nonlocal Cahn-Hilliard (NCH) equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard (LCH) equation. In this paper, based on the exponential semi-imp…

The stabilized exponential-SAV approach preserving maximum bound principle for nonlocal Allen-Cahn equation Open

Xiaoqing Meng, Aijie Cheng, Zhengguang Liu · 2023

The nonlocal Allen-Cahn equation with nonlocal diffusion operator is a generalization of the classical Allen-Cahn equation. It satisfies the energy dissipation law and maximum bound principle (MBP), and is important for simulating a series…

Synchronization of Coupled Phase Oscillators with Stochastic Disturbances and the Cycle Space of the Graph Open

Kaihua Xi, Zhen Wang, Aijie Cheng, Hai Xiang Lin, Jan H. van Schuppen , et al. · 2023

The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine …

Synchronization of power systems under stochastic disturbances Open

Zhen Wang, Kaihua Xi, Aijie Cheng, Hai Xiang Lin, André C. M. Ran , et al. · 2023

Explicit formulas for the Variance of the State of a Linearized Power System driven by Gaussian stochastic disturbances Open

Xian Wu, Kaihua Xi, Aijie Cheng, Hai Xiang Lin, Jan H. van Schuppen , et al. · 2023

We look into the fluctuations caused by disturbances in power systems. In the linearized system of the power systems, the disturbance is modeled by a Brownian motion process, and the fluctuations are described by the covariance matrix of t…

A Fast Finite Difference Method for 2d Time Fractional Mobile/Immobile Equation with Weaklysingular Solution Open

Haili Qiao, Aijie Cheng · 2023

Increasing the Synchronization Stability in Complex Networks Open

Xian Wu, Kaihua Xi, Aijie Cheng, Hai Xiang Lin, Jan H. van Schuppen · 2022

We aim to increase the ability of a of coupled phase oscillators to maintain the synchronization when the system is affected by stochastic disturbances. We model the disturbances by Gaussian noise and use the mean first hitting time when t…

Joint estimation of parameter and state with hybrid data assimilation and machine learning Open

Xiao Li, Cong Xiao, Aijie Cheng, Haixiang Lin · 2022

For parameter and state estimation problems, when observation is sparse and has large error covariance, the estimation results tend to have bias and lead to inaccurate forecasts further. To reduce the bias, we propose to construct a propos…

Synchronization of Coupled Phase Oscillators with Stochastic Disturbances and the Cycle Space of the Graph Open

Kaihua Xi, Zhen Wang, Aijie Cheng, Hai Xiang Lin, Jan H. van Schuppen , et al. · 2021

The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine …

A novel AlGaN/GaN heterostructure field-effect transistor based on open-gate technology Open

Yang Liu, Yuanjie Lv, Shuoshuo Guo, Zhengfang Luan, Aijie Cheng , et al. · 2021

A fast high order method for time fractional diffusion equation with non-smooth data Open

Haili Qiao, Aijie Cheng · 2021

In this paper, we consider the time fractional diffusion equation with Caputo fractional derivative. Due to the singularity of the solution at the initial moment, it is difficult to achieve an ideal convergence order on uniform meshes. The…

Finite Difference Method on Non-Uniform Meshes for Time Fractional Diffusion Problem Open

Haili Qiao, Aijie Cheng · 2020

In this paper, we consider the time fractional diffusion equation with Caputo fractional derivative. Due to the singularity of the solution at the initial moment, it is difficult to achieve an ideal convergence rate when the time discretiz…

Fast collocation method for a two-dimensional variable-coefficient linear nonlocal diffusion model Open

Xuhao Zhang, Aijie Cheng · 2020

A preconditioned fast collocation method for a linear bond-based peridynamic model Open

Xuhao Zhang, Xiao Li, Aijie Cheng, Hong Wang · 2020

A Fast Compact Finite Difference Method for Fractional Cattaneo Equation Based on Caputo–Fabrizio Derivative Open

Haili Qiao, Zhengguang Liu, Aijie Cheng · 2020

The Cattaneo equations with Caputo–Fabrizio fractional derivative are investigated. A compact finite difference scheme of Crank–Nicolson type is presented and analyzed, which is proved to have temporal accuracy of second order and spatial …

Two unconditionally stable difference schemes for time distributed-order differential equation based on Caputo–Fabrizio fractional derivative Open

Haili Qiao, Zhengguang Liu, Aijie Cheng · 2020

We consider distributed-order partial differential equations with time fractional derivative proposed by Caputo and Fabrizio in a one-dimensional space. Two finite difference schemes are established via Grünwald formula. We show that these…

A Preconditioned Fast Collocation Method for a Linear Nonlocal Diffusion Model in Convex Domains Open

Xuhao Zhang, Aijie Cheng, Hong Wang · 2020

Recently, there are many papers dedicated to develop fast numerical methods for nonlocal diffusion and peridynamic models. However, these methods require the physical domain where we solve the governing equations is rectangular. To relax t…

Theory of Second Order Numerical Simulation Method of Enhanced Oil Production Open

Yirang Yuan, Aijie Cheng, Danping Yang, Changfeng Li · 2019

A kind of second-order implicit upwind fractional steps finite difference method is presented in this paper to numerically simulate the coupled system of enhanced (chemical) oil production in porous media. Some techniques, such as the calc…

The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn-Hilliard equation Open

Zhengguang liu, Aijie Cheng, Xiaoli Li · 2019

Comparing with the classical local gradient flow and phase field models, the nonlocal models such as nonlocal Cahn-Hilliard equations equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase transi…

Effect of Polarization Coulomb Field Scattering on Electrical Properties of the 70-nm Gate-Length AlGaN/GaN HEMTs Open

Peng Cui, Yuanjie Lv, Fu Chen, Huan Liu, Aijie Cheng , et al. · 2018

This research presents the first experimental observation of the enhancement of the polarization Coulomb field (PCF) scattering by aggressive lateral scaling of GaN HEMTs. By decreasing the source-drain distance to 300 nm through n + -GaN …

Effect of Different Gate Lengths on Polarization Coulomb Field Scattering Potential in AlGaN/GaN Heterostructure Field-Effect Transistors Open

Peng Cui, Jianghui Mo, Fu Chen, Yuanjie Lv, Huan Liu , et al. · 2018

Improved Linearity with Polarization Coulomb Field Scattering in AlGaN/GaN Heterostructure Field-Effect Transistors Open

Peng Cui, Yuanjie Lv, Huan Liu, Aijie Cheng, Fu Chen , et al. · 2018

The single-tone power of the AlGaN/GaN heterostructure field-effect transistors (HFETs) with different gate widths was measured. A distinct improvement in device linearity was observed in the sample with a larger gate width. The analysis o…

Fast procedures for Caputo fractional derivative and its applications to ordinary and partial differential equations Open

Zhengguang Liu, Aijie Cheng, Xiaoli Li, Hong Wang · 2017

In this paper, we develop fast procedures for solving linear systems arising from discretization of ordinary and partial differential equations with Caputo fractional derivative w.r.t time variable. First, we consider a finite difference s…

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