A Fourier spectral scheme is proposed for solving the periodic problem of nonlinear Klein-Gordon equation. Its stability and convergence are investigated. Numerical results are also presented.
Split-step Padémethod and split-step fourier method are applied to the higher- order nonlinear Schrdinger equation.It is proved that a combination of Padé scheme and spectral method is the most effective met...Split-step Padémethod and split-step fourier method are applied to the higher- order nonlinear Schrdinger equation.It is proved that a combination of Padé scheme and spectral method is the most effective method,which has a spectral-like resolution and good stability nature.In particular,we propose an unconditional stable implicit Padé scheme to solve odd order nonlinear equations.Numerical results demonstrate the excellent performance of Padé schemes for high order nonlinear equations.展开更多
The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numer...The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numericalmethod and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventionalmulti-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.展开更多
文摘A Fourier spectral scheme is proposed for solving the periodic problem of nonlinear Klein-Gordon equation. Its stability and convergence are investigated. Numerical results are also presented.
基金This work is supported by the National Natural Science Foundations of Chinese under grant Nos, 10371118 and 90411009.
文摘Split-step Padémethod and split-step fourier method are applied to the higher- order nonlinear Schrdinger equation.It is proved that a combination of Padé scheme and spectral method is the most effective method,which has a spectral-like resolution and good stability nature.In particular,we propose an unconditional stable implicit Padé scheme to solve odd order nonlinear equations.Numerical results demonstrate the excellent performance of Padé schemes for high order nonlinear equations.
基金Jialin Hong is supported by the Director Innovation Foundation of ICMSEC and AMSS,the Foundation of CAS,the NNSFC(Nos.19971089,10371128 and 60771054)the Special Funds for Major State Basic Research Projects of China 2005CB321701+5 种基金Linghua Kong is supported by the NSFC(No.10901074)the Provincial Natural Science Foundation of Jiangxi(No.2008GQS0054)the Foundation of Department of Education of Jiangxi Province(No.GJJ09147)the Young Growth Foundation of Jiangxi Normal University(No.2390)the Doctor Foundation of Jiangxi Normal University(No.2057)State Key Laboratory of Scientific and Engineering Computing,CAS.
文摘The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numericalmethod and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventionalmulti-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.
