两类变时间步长的非线性Galerkin算法的稳定性

1．引言近年来，随着计算机的飞速发展，人们越来越关心非线性发展方程解的渐进行为．为了较精确地描述解在时间t→∞时的渐进行为，人们发展了一类惯性算法，即非线性Galerkin算法．该算法是将来解空间分解为低维部分和高维部分，相应的方程可以分别投影到它们上面，它的解也相应地分解为两部分，大涡分量和小涡分量；然后核算法给出大涡分量和小涡分量之间依赖关系的一种近似，以便容易求出相应的近似解．许多研究表明，非线性Galerkin算法比通常的Galerkin算法节省可观的计算量．当数值求解微分方程时，计算机只能对已知数据进行有限位…

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

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.