9 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,…