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Multisymplectic Methods for Long-Wave Short-Wave Interaction Equation

Author: ZhangYang
Tutor: WangJian
School: Shanghai Jiaotong University
Course: Computational Mathematics
Keywords: Multisymplectic methods Conservation laws Long-wave short-wave interaction equation
CLC: O241.6
Type: Master's thesis
Year: 2011
Downloads: 42
Quote: 0
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Abstract


This paper mainly is the study of multisymplectic methods for long and short wave interaction equation, which is the special form of Schrodinger-Kdv equations. It constructs Euler-box scheme, multisymplectic Preissman scheme and Fourier pseudospectral method to solve long- short wave interaction equation.These multisymplectic numerical methods are presented for the periodic initial-value problem of the long wave-short wave interaction equations. The first one is Euler box scheme, which is semi-explicit with second-order accuracy in space and first-order accuracy in time. The second one is the Preissman scheme, which is implicit with second-order accuracy in both space and time. The third on is Fourier pseudospectral method, which is of spectral-order accuracy in space and second-order accuracy in time. The important thing is that these new structures maintain symplectic structure of Hamilton system. Take different time and space steps in the numerical experiments to compare Euler box and Crank Nicolson scheme with multisymplectic Preissman scheme, to compare time split step method with Fourier pseudospectral method. And the structure of the three numerical formats all get the satisfactory results.

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