非线性发展方程的Taylor展开方法  

Taylor Expansion Method for the Nonlinear Evolution Equations

作　　者：何银年[1] 张鸿庆 许政范 

机构地区：[1]西安交通大学理学院，西安710049 [2]不详

出　　处：《应用数学和力学》2005年第4期481-488,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10371095);陕西省自然科学基金资助项目(2003A01)

摘　　要：　提出了积分非线性发展方程的新方法,即Taylor展开方法·　标准的Galerkin方法可以看作0＿阶Taylor展开方法,而非线性Galerkin方法可以看作1＿阶修正Taylor展开方法·　此外,证明了数值解的存在性及其收敛性·　结果表明,在关于严格解的一些正则性假设下,较高阶的Taylor展开方法具有较高阶的收敛速度·　最后。A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0_th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1_st order modified Taylor expansion method.Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example, namely the two_dimensional Navier_Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.

关 键 词：非线性发展方程 NAVIER-STOKES方程 Taylor展开方法 收敛速度 

分 类 号：O242.21[理学—计算数学]