- 教授
- 博士生导师
- 硕士生导师
- 电子邮箱：
- 入职时间：1997-07-01
- 学历：博士研究生毕业
- 性别：男
- 学位：博士
- 在职信息：在职
- 毕业院校：西安交通大学
- 所属院系：数学与统计学院
- 学科：数学
Semi-implicit Hermite-Galerkin spectral method for distributed- order fractional-in-space nonlinear reaction-diffusion equations in multidimensional unbounded domains
- 发布时间：2025-04-30
- 论文名称：Semi-implicit Hermite-Galerkin spectral method for distributed- order fractional-in-space nonlinear reaction-diffusion equations in multidimensional unbounded domains
- 发表刊物：Journal of Scientific Computing
- 摘要：In this paper, we construct an efficient Hermite-Galerkin spectral method for the nonlinear reaction diffusion equations with distributed-order fractional Laplacian in multidimensional unbounded domains. By applying Gauss-Legendre quadrature rule for the distributed integral term, we first approximate the original distributed-order fractional problem by the multi-term fractional-in-space differential equation. Applying Hermite-Galerkin spectral method in space and backward difference method in time, we establish semi-implicit
fully discrete scheme. For two- and three-dimensional cases of the original fractional problem, the linear systems are solved by the preconditioned conjugate gradients method. The main advantage of our method is that the original fractional problem is directly solved in the unbounded domains, thus avoiding the errors introduced by the domain truncations. The stability analysis is rigourously established, which shows that our scheme is unconditionally stable under suitable assumption on the nonlinear term. Several numerical examples are presented to validate both stability and accuracy of the numerical method. The numerical results of the fractional Allen-Cahn, Gray-Scott, and Belousov-Zhabotinskii models show that our semi-implicit methods produce good numerical solutions. - 合写作者：S. Guo, L. Mei, C. Li, Z. Zhang, Y. Li
- 卷号：85:15(2020)
- 是否译文：否
- 发表时间：2020-10-06
- 合写作者：S. Guo, L. Mei, C. Li, Z. Zhang, Y. Li