Search results for: Changpin Li

Items from 1 to 20 out of 79 results

article

A modified walk‐on‐sphere method for high dimensional fractional Poisson equation

Caiyu Jiao, Changpin Li, Hexiang Wang, Zhongqiang Zhang

Numerical Methods for Partial Differential Equations > 39 > 2 > 1128 - 1162

We develop walk‐on‐sphere method for fractional Poisson equations with Dirichilet boundary conditions in high dimensions. The walk‐on‐sphere method is based on probabilistic representation of the fractional Poisson equation. We propose efficient quadrature rules to evaluate integral representation in the ball and apply rejection sampling method to drawing from the computed probabilities in general...

article

Numerical algorithms for the time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations

Hengfei Ding, Changpin Li

Numerical Methods for Partial Differential Equations > 36 > 4 > 772 - 799

In this paper, high‐order numerical methods for time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations in one‐ and two‐dimensional space are constructed, where the second‐order backward fractional difference operator and the sixth‐order fractional‐compact difference operator are applied to approximate the time and space fractional derivatives, respectively. The stability and convergence of...

article

Preface to the Focused Issue on Fractional Derivatives and General Nonlocal Models

Qiang Du, Jan S. Hesthaven, Changpin Li, Chi-Wang Shu, more

Communications on Applied Mathematics and Computation > 2019 > 1 > 4 > 503-504

article

Modeling and Computing of Fractional Convection Equation

Changpin Li, Qian Yi

Communications on Applied Mathematics and Computation > 2019 > 1 > 4 > 565-595

In this paper, we derive the fractional convection (or advection) equations (FCEs) (or FAEs) to model anomalous convection processes. Through using a continuous time random walk (CTRW) with power-law jump length distributions, we formulate the FCEs depicted by Riesz derivatives with order in (0, 1). The numerical methods for fractional convection operators characterized by Riesz derivatives with order...

article

A High-Order Algorithm for Time-Caputo-Tempered Partial Differential Equation with Riesz Derivatives in Two Spatial Dimensions

Hengfei Ding, Changpin Li

Journal of Scientific Computing > 2019 > 80 > 1 > 81-109

A novel second-order numerical approximation for the Riemann–Liouville tempered fractional derivative, called the tempered fractional-compact difference formula is derived by using the tempered Grünwald difference operator and its asymptotic expansion. Using the relationship between Riemann–Liouville and the Caputo tempered fractional derivatives, then the constructed approximation formula is applied...

article

High-order numerical approximation formulas for Riemann–Liouville (Riesz) tempered fractional derivatives: Construction and application (II)

Hengfei Ding, Changpin Li

Applied Mathematics Letters > 2018 > 86 > C > 208-214

By constructing new numerical approximation formulas for the left and right Riemann–Liouville tempered fractional derivatives of order α ∈ ( 0 , 1 ) , a numerical algorithm is proposed to solve the space tempered fractional convection equation. The algorithm is shown to be unconditionally stable and convergent with order O τ 2 + h 2 . Finally, numerical example is provided to verify...

article

An alternating direction Galerkin method for a time-fractional partial differential equation with damping in two space dimensions

An Chen, Changpin Li

Advances in Difference Equations > 2017 > 2017 > 1 > 1-17

In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the sense of Caputo with order in ( 1 , 2 ) $(1,2)$ . The presented numerical scheme is based on the L2- 1 σ $1_{\sigma}$ method in time and the Galerkin finite element method in...

article

A new Crank–Nicolson finite element method for the time-fractional subdiffusion equation

Fanhai Zeng, Changpin Li

Applied Numerical Mathematics > 2017 > 121 > C > 82-95

In this paper, a new Crank–Nicolson finite element method for the time-fractional subdiffusion equation is developed, in which a novel time discretization called the modified L1 method is used to discretize the Riemann–Liouville fractional derivative. The present method is unconditionally stable and convergent of order O(τ1+β+hr+1), where β∈(0,1), τ and h are the step sizes in time and space, respectively,...

article

The finite difference method for Caputo-type parabolic equation with fractional Laplacian: One-dimension case

Ye Hu, Changpin Li, Hefeng Li

Chaos, Solitons & Fractals > 2017 > 102 > C > 319-326

In this paper, we present the finite difference method for Caputo-type parabolic equation with fractional Laplacian, where the time derivative is in the sense of Caputo with order in (0, 1) and the spatial derivative is the fractional Laplacian. The Caputo derivative is evaluated by the L1 approximation, and the fractional Laplacian with respect to the space variable is approximated by the Caffarelli–Silvestre...

article

Asymptotically compatible schemes for space-time nonlocal diffusion equations

An Chen, Qiang Du, Changpin Li, Zhi Zhou

Chaos, Solitons & Fractals > 2017 > 102 > C > 361-371

In this paper, we study a space-time nonlocal diffusion model that reduces to the classical diffusion equation in the local limit. Firstly, we show the uniqueness and existence of the weak solution of the nonlocal model, and study the local limit of the nonlocal model as horizon parameters approach zero. Particularly, it is shown that the convergence is uniform at a rate of O(δ+σ2), under certain...

article

High‐order algorithms for Riesz derivative and their applications (V)

Hengfei Ding, Changpin Li

Numerical Methods for Partial Differential Equations > 33 > 5 > 1754 - 1794

In this article, based on the idea of combing symmetrical fractional centred difference operator with compact technique, a series of even‐order numerical differential formulas (named the fractional‐compact formulas) are established for the Riesz derivatives with order

α \in (1, 2)

. Properties of coefficients in the derived formulas are studied in details. Then applying the constructed fourth‐order...

article

Pinning synchronization between two general fractional complex dynamical networks with external disturbances

Weiyuan Ma, Yujiang Wu, Changpin Li

IEEE/CAA Journal of Automatica Sinica > 2017 > 4 > 2 > 332 - 339

In this paper, the pinning synchronization between two fractional complex dynamical networks with nonlinear coupling, time delays and external disturbances is investigated. A Lyapunov-like theorem for the fractional system with time delays is obtained. A class of novel controllers is designed for the pinning synchronization of fractional complex networks with disturbances. By using this technique,...

article

High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions

Hengfei Ding, Changpin Li

Journal of Scientific Computing > 2017 > 71 > 2 > 759-784

A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich’s difference ones, which greatly improve the convergence orders and stability for time-dependent problems with Riesz derivatives. In rapid sequence, we apply the 2nd-order...

article

Finite difference methods with non-uniform meshes for nonlinear fractional differential equations

Changpin Li, Qian Yi, An Chen

Journal of Computational Physics > 2016 > 316 > C > 614-631

In this article, finite difference methods with non-uniform meshes for solving nonlinear fractional differential equations are presented, where the non-equidistant stepsize is non-decreasing. The rectangle formula and trapezoid formula are proposed based on the non-uniform meshes. Combining the above two methods, we then establish the predictor–corrector scheme. The error and stability analysis are...

article

High-order approximation to Caputo derivatives and Caputo-type advection–diffusion equations (III)

Hefeng Li, Jianxiong Cao, Changpin Li

Journal of Computational and Applied Mathematics > 2016 > 299 > C > 159-175

In this paper, a series of new high-order numerical approximations to αth (0<α<1) order Caputo derivative is constructed by using rth degree interpolation approximation for the integral function, where r≥4 is a positive integer. As a result, the new formulas can be viewed as the extensions of the existing jobs (Cao et al., 2015; Li et al., 2014), the convergence orders are O(τr+1−α), where τ...

chapter

Synchronization Analysis of Two Networks

Changpin Li, Weigang Sun

New Trends in Nanotechnology and Fractional Calculus Applications > Mathematical tools > 243-253

In this chapter we study synchronization for two coupled networks. Synchronization conditions between two networks which have same topological connectivity are derived. Then numerical examples are given to demonstrate that synchronization between two networks with directed or undirected topological connections can be achieved.

article

High‐order compact difference schemes for the modified anomalous subdiffusion equation

Hengfei Ding, Changpin Li

Numerical Methods for Partial Differential Equations > 32 > 1 > 213 - 242

In this article, two kinds of high‐order compact finite difference schemes for second‐order derivative are developed. Then a second‐order numerical scheme for a Riemann–Liouvile derivative is established based on a fractional centered difference operator. We apply these methods to a fractional anomalous subdiffusion equation to construct two kinds of novel numerical schemes. The solvability, stability,...

article

High-order algorithms for Riesz derivative and their applications (II)

Hengfei Ding, Changpin Li, YangQuan Chen

Journal of Computational Physics > 2015 > 293 > Complete > 218-237

In this paper, we firstly develop two high-order approximate formulas for the Riesz fractional derivative. Secondly, we propose a temporal second order numerical method for a fractional reaction-dispersion equation, where we discretize the Riesz fractional derivative by using two numerical schemes. We prove that the numerical methods for a spatial Riesz fractional reaction dispersion equation are...

chapter

Multi-UAV-based optimal crop-dusting of anomalously diffusing infestation of crops

Jianxiong Cao, YangQuan Chen, Changpin Li

2015 American Control Conference (ACC) > 1278 - 1283

2015 American Control Conference (ACC)

This paper presents a UAV-based optimal cropdusting method to control anomalously diffusing infestation of crops. Two anomalous diffusion models are considered, which are, respectively, time-fractional order diffusion equation and space-fractional order diffusion equation. Our problem formulation is motivated by real-time pest management by using networked unmanned cropdusters where the pest spreading...

article

On defining the distributions δk and (δ′)k by fractional derivatives

Chenkuan Li, Changpin Li

Applied Mathematics and Computation > 2014 > 246 > Complete > 502-513

How to define products and powers of distributions is a difficult and not completely understood problem, and has been investigated from several points of views since Schwartz established the theory of distributions around 1950. Many fields, such as differential equations or quantum mechanics, require such operations. In this paper, we use Caputo fractional derivatives and the following generalized...

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INFONA - science communication portal

Search results for: Changpin Li

A modified walk‐on‐sphere method for high dimensional fractional Poisson equation

Numerical algorithms for the time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations

Preface to the Focused Issue on Fractional Derivatives and General Nonlocal Models

Modeling and Computing of Fractional Convection Equation

A High-Order Algorithm for Time-Caputo-Tempered Partial Differential Equation with Riesz Derivatives in Two Spatial Dimensions

High-order numerical approximation formulas for Riemann–Liouville (Riesz) tempered fractional derivatives: Construction and application (II)

An alternating direction Galerkin method for a time-fractional partial differential equation with damping in two space dimensions

A new Crank–Nicolson finite element method for the time-fractional subdiffusion equation

The finite difference method for Caputo-type parabolic equation with fractional Laplacian: One-dimension case

Asymptotically compatible schemes for space-time nonlocal diffusion equations

High‐order algorithms for Riesz derivative and their applications (V)

Pinning synchronization between two general fractional complex dynamical networks with external disturbances

High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions

Finite difference methods with non-uniform meshes for nonlinear fractional differential equations

High-order approximation to Caputo derivatives and Caputo-type advection–diffusion equations (III)

Synchronization Analysis of Two Networks

High‐order compact difference schemes for the modified anomalous subdiffusion equation

High-order algorithms for Riesz derivative and their applications (II)

Multi-UAV-based optimal crop-dusting of anomalously diffusing infestation of crops

On defining the distributions δk and (δ′)k by fractional derivatives

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