Abstract A Legendre-tau-Galerkin method is developed for nonlinear evolution problems and its multiple interval form is also considered. The Legendre tau method is applied in time and the Legendre/Chebyshev–Gauss–Lobatto points are adopted to deal with the nonlinear term. By taking appropriate basis functions, it leads to a simple discrete equation. The proposed method enables us to derive optimal error estimates in L 2 -norm for the Legendre collocation under the two kinds of Lipschitz conditions, respectively. Our method is also applied to the numerical solutions of some nonlinear partial differential equations by using the Legendre Galerkin and Chebyshev collocation in spatial discretization. Numerical examples are given to show the efficiency of the methods.

中文翻译：

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非线性演化方程的Legendre-tau-Galerkin与谱配置方法

摘要 针对非线性演化问题，提出了Legendre-tau-Galerkin方法，并考虑了其多区间形式。及时应用Legendre tau方法，采用Legendre/Chebyshev-Gauss-Lobatto点处理非线性项。通过采用适当的基函数，可以得到一个简单的离散方程。所提出的方法使我们能够分别在两种Lipschitz 条件下为Legendre 搭配推导出L 2 -范数的最佳误差估计。通过在空间离散化中使用Legendre Galerkin和Chebyshev搭配，我们的方法还应用于一些非线性偏微分方程的数值解。给出了数值例子来显示方法的效率。