【摘要】 该文分析了广义Korteweg deVries(KdV)方程非周期边值问题的Legendre Petrov GalerkinChebyshev配置(LPG CC)方法,其中非线性项用Chebyshev配置方法来逼近,时间方向上采用Crank Nicolson离散格式.对于半离散和全离散格式,都获得了关于L2 范数的最优误差估计.更多还原

【Abstract】 In this paper, the Legendre-Petrov-Galerkin method for the Generalized Korteweg-de Vries equation with nonperiodic boundary conditions is analyzed. The nonlinear term is computed with the Chebyshev collocation method. Crank-Nicolson scheme is applied to the time space, optimal error (estimates) in L~2-norm are obtained for semi-discrete and fully-discrete schemes.更多还原