- 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
A linearized spectral-Galerkin method for three-dimensional Riesz-like space fractional nonlinear coupled reaction-diffusion equations
- 发布时间：2025-04-30
- 论文名称：A linearized spectral-Galerkin method for three-dimensional Riesz-like space fractional nonlinear coupled reaction-diffusion equations
- 发表刊物：Numerical Mathematics: Theory, Methods and Applications
- 摘要：In this paper, we establish a novel fractional model arising in the chemical reaction and develop an e cient spectral method for the three-dimensional Riesz-like space fractional nonlinear coupled reactiondiffusion equations. Based on the backward di erence method for time stepping and the Legendre-Galerkin spectral method for space discretization, we construct a fully discrete numerical scheme which leads to a linear algebraic system. Then a direct method based on the matrix diagonalization approach is proposed to solve the linear algebraic system, where the cost of the algorithm is of a small multiple of N4 (N is the polynomial degree in each spatial coordinate) ops for each time level. In addition, the stability and convergence analysis are rigorously established. We obtain the optimal error estimate in space, and the results also show that the fully discrete scheme is unconditionally stable and convergent of order one in time. Furthermore, numerical experiments are presented to con rm the theoretical claims. As the applications of the proposed method, the fractional Gray-Scott model is solved to capture the pattern formation with an analysis of the properties of the fractional powers.
- 合写作者：S. Guo, W. Yan, L. Mei, Y. Wang, L. Wang
- 卷号：14(4)
- 是否译文：否
- 发表时间：2021-07-01
- 合写作者：S. Guo, W. Yan, L. Mei, Y. Wang, L. Wang
上一条：Numerical approximation of the two-component PFC models for binary colloidal crystals: efficient, decoupled, and second-order unconditionally energy stable schemes
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