On Time-Splitting Pseudospectral Discretization for Nonlinear Klein-Gordon Equation in Nonrelativistic Limit Regime

作     者：Xuanchun Dong Zhiguo Xu Xiaofei Zhao 

作者机构：Beijing Computational Science Research CenterBeijing 100084P.R.China Department of MathematicsNational University of SingaporeSingapore 119076Singapore College of MathematicsJilin UniversityChangchun 130012P.R.China 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2014年第16卷第7期

页      面：440-466页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：supported by the Singapore A*STAR SERC PSF-Grant 1321202067 

主　　题：Klein-Gordon equation high oscillation time-splitting trigonometric integrator error estimate meshing strategy. 

摘      要：In this work,we are concerned with a time-splitting Fourier pseudospectral(TSFP)discretization for the Klein-Gordon(KG)equation,involving a dimensionless parameterε∈(0,1].In the nonrelativistic limit regime,the smallεproduces high oscillations in exact solutions with wavelength of O(ε^(−2))in *** key idea behind the TSFP is to apply a time-splitting integrator to an equivalent first-order system in time,with both the nonlinear and linear subproblems exactly integrable in time and,respectively,Fourier frequency *** method is fully explicit and time ***,we establish rigorously the optimal error bounds of a second-order TSFP for fixedε=O(1),thanks to an observation that the scheme coincides with a type of trigonometric *** the second task,numerical studies are carried out,with special effortsmade to applying the TSFP in the nonrelativistic limit regime,which are geared towards understanding its temporal resolution capacity and meshing strategy for O(ε^(−2))-oscillatory solutions when 0ε≪*** suggests that the method has uniform spectral accuracy in space,and an asymptotic O(ε^(−2)D^(t2))temporal discretization error bound(Dt refers to time step).On the other hand,the temporal error bounds for most trigonometric integrators,such as the well-established Gautschi-type integrator in[6],are O(ε^(−4)D^(t2)).Thus,our method offers much better approximations than the Gautschi-type integrator in the highly oscillatory *** results,either rigorous or numerical,are valid for a splitting scheme applied to the classical relativistic NLS reformulation as well.