14 citations · 28 across the 13 of their papers we have counts for
13 papers
Correction of weighted and shifted seven-step BDF for parabolic equations with nonsmooth data
Minghua Chen, Jiankang Shi, Fan Yu +1
It is well known that the seven-step backward difference formula (BDF) is unstable for the parabolic equations, since it is not even zero-stable. However, a linear combination of t…
A Second-order method on graded meshes for fractional Laplacian via Riesz fractional derivative with a singular source term
Minghua Chen, Jianxing Han, Jiankang Shi +1
The high-order numerical analysis for fractional Laplacian via the Riesz fractional derivative, under the low regularity solution, has presented significant challenges in the past…
Error analysis of a collocation method on graded meshes for nonlocal diffusion problems with weakly singular kernels
Minghua Chen, Chao Min, Jiankang Shi +1
Can graded meshes yield more accurate numerical solution than uniform meshes? A time-dependent nonlocal diffusion problem with a weakly singular kernel is considered using collocat…
High-order BDF convolution quadrature for stochastic fractional evolution equations driven by integrated additive noise
Minghua Chen, Jiankang Shi, Zhen Song +2
The numerical analysis of stochastic time fractional evolution equations presents considerable challenges due to the limited regularity of the model caused by the nonlocal operator…
High-order BDF convolution quadrature for fractional evolution equations with hyper-singular source term
Jiankang Shi, Minghua Chen, Jianxiong Cao
Anomalous diffusion in the presence or absence of an external force field is often modelled in terms of the fractional evolution equations, which can involve the hyper-singular sou…
High-order BDF convolution quadrature for subdiffusion models with a singular source term
Jiankang Shi, Minghua Chen
Anomalous diffusion is often modelled in terms of the subdiffusion equation, which can involve a weakly singular source term. For this case, many predominant time stepping methods,…
Modified BDF2 schemes for subdiffusion models with a singular source term
Minghua Chen, Jiankang Shi, Zhi Zhou
The aim of this paper is to study the time stepping scheme for approximately solving the subdiffusion equation with a weakly singular source term. In this case, many popular time s…
Correction of high-order approximation for subdiffusion
Jiankang Shi, Minghua Chen, Yubin Yan +1
The subdiffusion equations with a Caputo fractional derivative of order arise in a wide variety of practical problems, which is describing the transport processes, in…
Analysis of (shifted) piecewise quadratic polynomial collocation for nonlocal diffusion model
Minghua Chen, Jiankang Shi, Xiaobo Yin
The piecewise quadratic polynomial collocation is used to approximate the nonlocal model, which generally obtain the {\em nonsymmetric indefinite system} [Chen et al., IMA J. Numer…
Correction of BDFk for fractional Feynman-Kac equation with Lévy flight
Jiankang Shi, Minghua Chen
In this work, we present the correction formulas of the -step BDF convolution quadrature at the starting steps for the fractional Feynman-Kac equation with Lévy flight. Th…
A sharp error estimate of piecewise polynomial collocation for nonlocal problems with weakly singular kernels
Minghua Chen, Wenya Qi, Jiankang Shi +1
As is well known, using piecewise linear polynomial collocation (PLC) and piecewise quadratic polynomial collocation (PQC), respectively, to approximate the weakly singular integra…
A second-order accurate scheme for two-dimensional space fractional diffusion equations with time Caputo-Fabrizio fractional derivative
Jiankang Shi, Minghua Chen
We provide and analyze a second order scheme for the model describing the functional distributions of particles performing anomalous motion with exponential Debye pattern and no-ti…
High order algorithms for Fokker-Planck equation with Caputo-Fabrizio fractional derivative
Minghua Chen, Jiankang Shi, Weihua Deng
Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenom…