Taylor Expansion Method for the Nonlinear Evolution Equations
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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A·D2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.
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关键词:
- 非线性发展方程 /
- Navier-Stokes方程 /
- Taylor展开方法 /
- 收敛速度
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. -
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