【摘要】 针对带有周期边值条件的非线性Schrdinger方程提出了保持能量守恒的半离散和全离散Fourier谱逼近格式,讨论了全离散格式解的存在惟一性条件,并分别进行了误差估计。由于采用全离散逼近格式得出的离散方程对每个时间步是非线性代数方程,本文对它采用预估-校正算法求解,并用数值试验证实了该逼近格式与算法的有效性和可行性。更多还原

【Abstract】 Fourier seimdiscrete and fully discrete schemes that inherit the conservation properties of differential equation are presented to numerically solve the nonlinear Schrdinger equation with periodic boundary conditions.The conditions under which the fully discrete form has a unique solution are discussed and the error estimates are analyzed.The implement of the fully discrete scheme requires the solution of a nonlinear system of equations at each time step.The theoretical results are confirmed by numerical experiments using the predictor-corrector algorithm.更多还原