5 papers
On spectral Petrov-Galerkin method for solving fractional initial value problems in weighted Sobolev space
Shengyue Li, Wanrong Cao, Zhaopeng Hao
In this paper, we investigate a spectral Petrov-Galerkin method for fractional initial value problems. Singularities of the solution at the origin inherited from the weakly singula…
On spectral Petrov-Galerkin method for solving optimal control problem governed by a two-sided fractional diffusion equation
Shengyue Li, Wanrong Cao, Yibo Wang
In this paper, we investigate a spectral Petrov-Galerkin method for an optimal control problem governed by a two-sided space-fractional diffusion-advection-reaction equation. Takin…
Implicit-Explicit difference schemes for nonlinear fractional differential equations with non-smooth solutions
Wanrong Cao, Fanhai Zeng, Zhongqiang Zhang +1
We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order . From the known structure of th…
A second-order difference scheme for the time fractional substantial diffusion equation
Zhaopeng Hao, Wanrong Cao, Guang Lin
In this work, a second-order approximation of the fractional substantial derivative is presented by considering a modified shifted substantial Grünwald formula and its asymptotic e…
An improved algorithm based on finite difference schemes for fractional boundary value problems with non-smooth solution
Zhao-Peng Hao, Wan-Rong Cao
In this paper, an efficient algorithm is presented by the extrapolation technique to improve the accuracy of finite difference schemes for solving the fractional boundary value pro…