非线性Galerkin算法和Galerkin算法

Nonlinear Galerkin Algorithm and Galerkin Algorithm

给出了数值求解非线性发展方程的Ｇａｌｅｒｋｉｎ算法和非线性Ｇａｌｅｒｋｉｎ算法，其中空间变量用谱元法离散，时间变量用Ｅｕｉｅｒ显式格式离散。此外，我们分析了两种算法的有界性、稳定性和收敛精度估计。经过比较，在收敛精度相同的条件下，非线性Ｇａｌｅｒｋｉｎ算法具有稳定性能好。

In this paper,we provide Galerkin algorithm and nonlinear Galerkin algorithm for solving the nonlinear evolution equations,where the spatial variable discretization is performed by Galerkin spectral element method and nonlinear Galerkin spectral element method and the time variable discretization is made by Euier explicit scheme Moreover,we analyse the boundedness,stability and convergence accuracy of these algorithms By comparison,we come to the condusion that under the same convergence accuracy,the computational time and stability of nonlinnear Galerkin algorithm are prior to the ones of Galerkin algorithm