Fisher型方程的Jacobi谱配点法（英文）

Solving Fisher-type equations by Jacobi spectral collocation method

主要讨论了以Jacobi-Gauss-Lobatto点为配置点的谱配点法数值求解具有初边值条件的Fisher型方程.借助于插值和由此产生的微分矩阵,将Fisher型方程转化为常微分方程组,再利用四阶Runge-Kutta法求解该常微分方程组.文中以一维Fisher型方程为例证明了该方法具有谱精度,并给出了四个Fisher型方程算例.数值例子验证了Jacobi谱配点法具有高精度和快速收敛性.

The aim of this paper is to obtain the numerical solutions to the Fisher-type equations with initial-boundary conditions by the Jacobi spectral collocation method using the Jacobi-Gauss-Lobatto collocation(JGLC)points.By means of the interpolation and the resulting differentiation matrix,we transfer the nonlinear partial differential equations into a system of ordinary differential equations(ODEs)that can be solved by the fourth-order Runge-Kutta method.We prove the spectral accuracy of this method for one-dimensional Fisher-type equations.Four examples of the Fisher-type equations are considered,and numerical experiments demonstrate the high accuracy and the fast convergence of the Jacobi spectral collocation method.