Da Xu

Hunan Normal University

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Wenlin Qiu

Hunan Normal University

Xuehua Yang

Hunan University of Technology

Leijie Qiao

Shanxi University

Haixiang Zhang

Hunan University of Technology

Jing Guo

Hunan Normal University

Jun Zhou

Central South University of Forestry and Technology

Hongbin Chen

Central South University of Forestry and Technology

Man Luo

Hunan Women'S University

Tao Guo

Hunan Normal University

Limei Li

Hunan Institute of Science and Technology

Cooperative Institutions

Hunan Normal University

Central South University

Central South University of Forestry and Technology

Xiangtan University

Commonwealth Scientific and Industrial Research Organisation

Centre National de la Recherche Scientifique

Harbin Engineering University

Tsinghua University

Changsha University of Science and Technology

Harbin Institute of Technology

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Numerical solution of partial integro-differential equation with a weakly singular kernel based on Sinc methods

Mathematics and Computers in Simulation (2021)

Da Xu

Sinc function

Collocation (remote sensing)

Kernel (algebra)

Regular singular point

Singular solution

10.1016/j.matcom.2021.05.014

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Citations (7)

Numerical analysis of Volterra integro-differential equations for viscoelastic rods and membranes

Applied Mathematics and Computation (2019)

Da Xu

Rod

Volterra equations

10.1016/j.amc.2019.02.064

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Citations (1)

Crank-Nicolson Quasi-Wavelet Based Numerical Method for Volterra Integro-Differential Equations on Unbounded Spatial Domains

East Asian Journal on Applied Mathematics (2013)

Man Luo Da Xu Limei Li

Abstract The numerical solution of a parabolic Volterra integro-differential equation with a memory term on a one-dimensional unbounded spatial domain is considered. A quasi-wavelet based numerical method is proposed to handle the spatial discretisation, the Crank-Nicolson scheme is used for the time discretisation, and second-order quadrature to approximate the integral term. Some numerical examples are presented to illustrate the efficiency and accuracy of this approach.

Crank–Nicolson method

Quadrature (astronomy)

10.4208/eajam.170813.131013a

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Citations (1)

An efficient Sinc-collocation method via the DE transformation for eighth-order boundary value problems

Journal of Computational and Applied Mathematics (2022)

Wenlin Qiu Da Xu Jun Zhou Jing Guo

Sinc function

Collocation (remote sensing)

Ode

10.1016/j.cam.2022.114136

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Citations (6)

High‐order ADI orthogonal spline collocation method for a new 2D fractional integro‐differential problem

Mathematical Methods in the Applied Sciences (2020)

Leijie Qiao Da Xu Yubin Yan

We use the generalized L1 approximation for the Caputo fractional derivative, the second‐order fractional quadrature rule approximation for the integral term, and a classical Crank‐Nicolson alternating direction implicit (ADI) scheme for the time discretization of a new two‐dimensional (2D) fractional integro‐differential equation, in combination with a space discretization by an arbitrary‐order orthogonal spline collocation (OSC) method. The stability of a Crank‐Nicolson ADI OSC scheme is rigourously established, and error estimate is also derived. Finally, some numerical tests are given.

Quadrature (astronomy)

Crank–Nicolson method

Collocation (remote sensing)

Spline (mechanical)

Orthogonal collocation

10.1002/mma.6258

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Citations (12)

A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation

Computers & Mathematics with Applications (2022)

Haixiang Zhang Xuehua Yang Qiong Tang Da Xu

Orthogonal collocation

Collocation (remote sensing)

Spline (mechanical)

10.1016/j.camwa.2022.01.007

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Citations (41)

An efficient Sinc‐collocation method by the single exponential transformation for the nonlinear fourth‐order partial integro‐differential equation with multiterm kernels

Mathematical Methods in the Applied Sciences (2021)

Huifa Jiang Da Xu

In this article, a Sinc‐collocation method is proposed and analyzed for solving the nonlinear fourth‐order partial integro‐differential equation with the multiterm kernels. The time derivative is discretized by the backward Euler method, and the Riemann–Liouville (R‐L) fractional integral terms are treated by means of the first‐order convolution quadrature. Then, the nonlinear term is linearized. A fully discrete scheme is established with the space discretization by the Sinc approximation based on the single exponential (SE) transformation. The spatial exponential convergence of the proposed method is derived. Several numerical examples are provided to illustrate the accuracy and effectiveness of our method.

Sinc function

Quadrature (astronomy)

Convolution (computer science)

10.1002/mma.7984

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Citations (2)

Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations

Boundary Value Problems (2024)

Man Luo Da Xu Xianmin Pan

Sinc function

10.1186/s13661-024-01915-6

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Citations (0)

Research on Dynamic Targets Tracking Based on Color Cues Under Complicated Scene

Zenodo (CERN European Organization for Nuclear Research) (2011)

Yi Wang Yang Fang Da Xu Suephy C. Chen Hui Wang

Abstract Compared with DST, DSmT can be good evidence of contradictions to resolve the issue of evidence portfolios, In view of the occluding in tracking dynamic targets in complex background, a new anti-occluding target tracking algorithm based on DSmT and particle filter is proposed by color cues. The simulation results show that the proposed algorithm is effective and practicable in tracking occluded target and intersected target. Compared with the existing combination rules, the newly proposed rule is applied to both cases of conflicting and coincidence

Tracking (education)

Sensory cue

10.5281/zenodo.237148

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Citations (0)

The Crank-Nicolson-type Sinc-Galerkin method for the fourth-order partial integro-differential equation with a weakly singular kernel

Applied Numerical Mathematics (2020)

Wenlin Qiu Da Xu Jing Guo

Sinc function

Kernel (algebra)

Quadrature (astronomy)

Crank–Nicolson method

10.1016/j.apnum.2020.09.011

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Citations (35)