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Numerical Methods of Nonlinear Schr(?)dinger Equation

Author: WangXiuFeng
Tutor: ZhangChuanLin
School: Jinan University
Course: Basic mathematics
Keywords: Nonlinear Schr (o ¨) dinger equation Numerical stability Local truncation error Frozen Coefficient Method Hamiltonian system Symplectic algorithm
CLC: O241.82
Type: Master's thesis
Year: 2006
Downloads: 492
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Abstract


In this paper, a nonlinear Schr ( ? ) Dinger equation by the numerical solution of two categories : the finite difference method and the symplectic algorithm and nonlinear Schr (?) Dinger equation symplectic algorithm is extended to high -dimensional . First, the nonlinear Schr ( ? ) Dinger equation seven differential format : second-order two - tier format , the second two-tier format alternating explicit-implicit format , the fourth-order two-tier format , the fourth-order two-tier format alternately explicit-implicit format , second order leapfrog format , fourth order leapfrog format and three implicit format . This the seven difference scheme local truncation error analysis and analysis of their stability , and the use of a \Next by numerical experiments verify their stability, compared with their computation time and accuracy . Then prove nonlinear Hamiltonian systems the Euler midpoint of the format , and leapfrog format Singh - specific given the nonlinear Schr ( ? ) Dinger equation of the second order Euler midpoint of the format , the fourth-order Euler midpoint format , second order leapfrog format and fourth-order leapfrog format and made ​​numerical experiments to verify the feasibility of these formats and compare the error . Next, compare a Singh - and a non- symplectic difference scheme of the same order of truncation error . We select the second-order the leapfrog format and the second two-tier format made ​​numerical experiments , and they run results were compared . Finally, the nonlinear Schr (?) Dinger equation Singh promotion to high -dimensional , and are given a special nonlinear Schr (?) Dinger equation - Nonlinear Hyperbolic Schr ( ? ) Dinger equation the second-order leapfrog format and numerical experiments to verify its feasibility .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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