4 papers · 1 filter
Nonlinear parametrization solver for fractional Burgers equations
Haojun Qin, Zhiwei Gao, Jinye Shen +1
Fractional Burgers equations pose substantial challenges for classical numerical methods due to the combined effects of nonlocality and shock-forming nonlinear dynamics. In particu…
Approximating and preconditioning the stiffness matrix in the GoFD approximation of the fractional Laplacian
Weizhang Huang, Jinye Shen
In the finite difference approximation of the fractional Laplacian the stiffness matrix is typically dense and needs to be approximated numerically. The effect of the accuracy in a…
A moving mesh finite element method for Bernoulli free boundary problems
Jinye Shen, Heng Dai, Weizhang Huang
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a…
Meshfree finite difference solution of homogeneous Dirichlet problems of the fractional Laplacian
Jinye Shen, Bowen Shi, Weizhang Huang
A so-called grid-overlay finite difference method (GoFD) was proposed recently for the numerical solution of homogeneous Dirichlet boundary value problems of the fractional Laplaci…