【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,给出了用Taylor展开方法求解二维具有非滑移边界条件Navier＿Stokes方程的具体例子·更多还原

【Abstract】 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.更多还原