谱配置法求解常微分方程初值问题的超收敛性

Superconvergence of spectral collocation method for initial value problem of ordinary differential equations

研究了常微分方程初值问题的谱配置方法.针对一阶和二阶线性常微分方程初值问题,基于Legendre-Gauss点提出了相应的谱配置方法,并给出了具体的计算格式.最后,通过一些数值算例探讨了所提Legendre-Gauss谱配置方法的超收敛性.

In this paper,we study the spectral collocation method for the initial value problems of ordinary differential equations.Based on Legendre-Gauss points,we propose the spectral collocation method for the initial value problems of first-order and second-order.We also give the specific computation form for our method.Finally,to explain the superconvergence properties of the Legendre-Gauss spectral collocation method.We discuss several numerical examples.