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With five times the nonlinear Schr ( ? ) Dinger equation Sim and multi-symplectic algorithm

Author: XuJinPing
Tutor: DanShuangRong
School: Huaqiao University
Course: Basic mathematics
Keywords: Singh - The law of conservation of energy Momentum conservation law Multi - symplectic conservation law Nonlinear Schr ( O ¨ ) dinger equation
CLC: O241.82
Type: Master's thesis
Year: 2009
Downloads: 10
Quote: 0
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Abstract


1984 of computational mathematics founder of Feng Kang Yuanshi the first time raised the symplectic structure of the Hamiltonian system to maintain constant symplectic In recent years , this algorithm has been rapid development and successfully solve many practical problems to simulate a variety of physical phenomena . consider with five nonlinear Schr ? dinger equation ( single ) Sim and multi-symplectic algorithm to construct the equation (single ) Singh , multi - Preissman Scheme and multi-symplectic the Fourier pseudospectral format the first chapter is an introduction part , a brief introduction of the the symplectic algorithm development history and current situation , as well as some research in this area . discussed in the second chapter with five nonlinear Schr ? dinger equation (single ) symplectic algorithm to construct the (single ) Singh , a numerical experiment is to verify the format has long numerical simulation capability . third chapter begins with a brief introduction to multi-symplectic Hamiltonian system and its related conservation laws , and then to construct the with five nonlinear Schr ? dinger equation Preissman Scheme to prove that this multi-symplectic schemes to maintain the conservation of charge , the energy error analysis of the stability of the format and using the energy method and convergence. Finally, a numerical experiment to verify our theoretical analysis is correct , that the format has long numerical stability . fourth chapter begins with a brief introduction to multi - symplectic Fourier pseudo-spectral method of prior knowledge and constructed with five times the nonlinear Schr ? dinger equation Multisymplectic Fourier pSEUDOSPECTRAL format , Finally , a numerical example illustrates the effectiveness of the format the fifth chapter, the main contents of the full text of the brief summary of the ( single ) Sim and the future direction of the multi-symplectic algorithm to do some Prospects .

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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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