Publications/学术论文 - 梅 立泉
论文标题 | An efficient Galerkin spectral method for two-dimensional fractional nonlinear reaction-diffusion-wave equation |
作者 | Shimin Guo; Liquan Mei; Ying Li |
发表/完成日期 | 2017-11-15 |
期刊名称 | Computers and Mathematics with Applications |
期卷 | |
相关文章 | |
论文简介 | The aim of this paper is to develop an efficient numerical treatment for the two-dimensional fractional nonlinear reaction-diffusion-wave equation with the time-fractional derivative of order α (1 < α < 2). For this purpose, we employ the alternating direction implicit (ADI) method based on the Crank-Nicolson scheme for the time stepping, while we apply the Legendre-Galerkin spectral method for the space discretization. The stability and convergence analysis are rigorously set up. In addition, the proposed method is extended to solve the time-fractional Klein-Gordon and sine-Gordon models. Numerical experiments are included, which verifies the theoretical predictions. |