基于Matlab求解反应扩散方程的一种数值方法  

Numerical method for solving reaction-diffusion equations based on Matlab

作　　者：王红玉 WANG Hongyu(Jinzhou Medical University,Jinzhou,Liaoning 121001,China)

机构地区：[1]锦州医科大学,辽宁锦州121001

出　　处：《计算机应用文摘》2025年第7期253-255,共3页

摘　　要：文章对反应扩散方程进行了数值模拟研究。首先,采用傅里叶谱方法对空间方向上的导数进行离散,将原方程转化为仅与时间相关的常微分方程。随后,利用四阶龙格-库塔法对该常微分方程组进行时间离散,建立了一种求解非定常反应扩散问题的有效数值方法。基于该方法,对几种常见的反应扩散模型进行了数值模拟。模拟结果表明,在保持其他条件不变的情况下,通过调节控制参数的取值,系统能够对图灵斑图的形成产生显著影响。This article conducted numerical simulation research on the reaction-diffusion equation.Firstly,the Fourier spectral method is used to discretize the derivatives in the spatial direction,transforming the original equation into an ordinary differential equation that is only time-dependent.Subsequently,the fourth-order Runge Kutta method was used to discretize the system of ordinary differential equations in time,establishing an effective numerical method for solving unsteady reaction-diffusion problems.Based on this method,numerical simulations were conducted on several common reaction-diffusion models.The simulation results indicate that,while keeping other conditions constant,the system can significantly affect the formation of Turing patterns by adjusting the values of control parameters.

关 键 词：反应扩散方程 斑图 傅里叶谱方法 四阶龙格-库塔法 

分 类 号：O241[理学—计算数学]