基于二元三次B样条拟插值的反应-扩散方程数值解

Numerical Solutions of Reaction-Diffusion Equations Based on Bivariate Cubic B-spline Quasi-Interpolation

反应-扩散方程在科学和工程的许多分支中有着重要的应用,对此类方程数值解的研究具有重要意义.鉴于计算域的复杂形状、大量的自由度等导致计算非常困难,提出张量积型二元三次B样条法求解一类分数阶反应-扩散方程和交叉反应扩散系统,首先计算得出二元三次B样条拟插值的矩阵表达式,然后利用Matlab进行数值模拟,最后将数值模拟解与精确解进行对比.研究表明,当变量t的迭代次数较低时,所提方法行之有效.

Reaction-diffusion equations have important applications in many branches of science and engineering.Therefore,it is of great significance to study the numerical solutions of such equations.In view of the complex shape for the computational domain and a large number of degrees of freedom,the calculation is very difficult.The tensor-product-typed bivariate cubic B-spline method is proposed to solve a class of fractional reaction-diffusion equations and cross-reaction-diffusion systems.First,the matrix expression of the bivariate cubic B-spline quasi-interpolation is calculated.Second it is numerically simulated by Matlab.Finally,the numerical simulation solution is compared with the exact solution,which shows that the method presented is effective when the number of iterations of the variables is low.