抛物方程的Legendre-Galerkin Chebyshev配置最小二乘法

Legendre-Galerkin Chebyshev Collocation Least Squares Method for Parabolic Equations

研究抛物方程的Legendre-Galerkin-Chebyshev配置(LGC)最小二乘方法以及其多区域格式.首先通过引进通量,将原问题变成等价的一阶系统.然后对一阶系统,该方法基于Legendre-Galerkin格式,对右端源项与初值部分则采用Chebyshev插值.数值实验显示该方法具有高阶谱精度.

The Legendre-Galerkin Chebyshev collocation least squares methods for parabolic equations is developed in this paper.We also consider its multi-intervals formulas.The original equation is rewritten into an equivalent first-order system by introducing a flux.The propose is based on the Legendre-Galerkin scheme,but the right hand side and the initial value terms are computed by Chebyshev collocation.Some numerical examples are given to test the accuracy of our schemes.