• 论文 •

### 求解极坐标系下反应扩散方程的紧致隐积分因子方法

1. 1. 沈阳师范大学 数学与系统科学学院, 沈阳 110034;
2. 广东工业大学 应用数学学院, 广州 510006
• 收稿日期:2019-12-11 发布日期:2021-06-03
• 通讯作者: 张荣培, Email: rongpeizhang@163.com.
• 基金资助:
辽宁省自然科学基金（20180550996）资助.

Huo Junrong, Zhang Rongpei. COMPACT IMPLICIT INTEGRATION FACTOR METHOD FOR SOLVING REACTION DIFFUSION EQUATION IN POLAR COORDINATE[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(2): 146-154.

### COMPACT IMPLICIT INTEGRATION FACTOR METHOD FOR SOLVING REACTION DIFFUSION EQUATION IN POLAR COORDINATE

Huo Junrong1, Zhang Rongpei2

1. 1. College of Mathematics and System Science, Shenyang Normal University, Shenyang 110034, China;
2. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China
• Received:2019-12-11 Published:2021-06-03

Reaction diffusion equations are widely used in physics, chemistry and biology. The previous work mainly considered the solution on the rectangular region. In this paper, the reaction-diffusion equations in circular and annular regions are studied. First, the reactiondiffusion equation is written in polar coordinate form, and the second-order finite difference method is used to discretize in spatial direction. The numerical solution on the grid is written in the matrix form, and the differential operator is discretized into matrix form, thus the nonlinear ordinary differential equations in compact form are obtained. Then the implicit integration factor method is used to solve the nonlinear ordinary differential equations. The compact implicit integral factor method not only reduces the storage, but also only needs to solve the local nonlinear algebraic equations at each time level. Finally, the numerical examples are given. The reaction-diffusion equation with exact solutions and Schnakenberg model are selected to solve on the circular and annular regions. The numerical results show that the computation with our method is efficient and accurate.

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