两类变时间步长的非线性Galerkin算法的稳定性  

THE STABILITY OF TWO TYPES OF NONLINEAR GALERKIN ALGORITHM WITH VARIABLE TIME STEPS

作　　者：何银年[1] 侯延仁[1] 

机构地区：[1]西安交通大学理学院

出　　处：《计算数学》1999年第2期139-156,共18页Mathematica Numerica Sinica

基　　金：国家自然科学基金;攀登计划资助

摘　　要：This paper reprents two types of fully discrete Galerkin algorithm and nonlinear Galerkin algoritlun with variable time steps for solving numerically nonlinear evolution equations, in which spatial discretization is made by spectral functions and finite elements; time is done by the Euler explicit difference scheme with the first order accuracy and two-step semi-implicit difference scheme with the second order accuracy. According to the stability analysis, we find that for the Euler difference scheme and two-step difference scheme on time discretization the stability of the fully discrete nonlinear Galerkin algorithms is superior to ones of the fully discrete Galerkin a-lgorithms. Finally, our numerical test also shows this fact.This paper reprents two types of fully discrete Galerkin algorithm and nonlinear Galerkin algoritlun with variable time steps for solving numerically nonlinear evolution equations, in which spatial discretization is made by spectral functions and finite elements; time is done by the Euler explicit difference scheme with the first order accuracy and two-step semi-implicit difference scheme with the second order accuracy. According to the stability analysis, we find that for the Euler difference scheme and two-step difference scheme on time discretization the stability of the fully discrete nonlinear Galerkin algorithms is superior to ones of the fully discrete Galerkin a-lgorithms. Finally, our numerical test also shows this fact.

关 键 词：变时间步长 稳定性 非线性 Galerkin乘法 

分 类 号：O241.82[理学—计算数学]