| 一类非线性伪抛物型方程的伪谱解法 |
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| 引用本文： | 刘霖雯,刘超,江成顺.一类非线性伪抛物型方程的伪谱解法[J].计算数学,2007,29(1):99-12. |
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| 作者姓名： | 刘霖雯 刘超 江成顺 |
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| 作者单位： | 1. 信息工程大学信息工程学院,郑州,450002
2. 大连理工大学海岸与近海工程国家重点实验室,辽宁大连,210023 |
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| 基金项目： | 国家自然科学基金
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河南省高等学校杰出人才创新工程项目
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大连理工大学校科研和教改项目 |
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| 摘 要： | 本文考虑了一类非线性伪抛物型方程的Fourier伪谱方法,建立了该方程的Fourier伪谱方法的半离散格式和全离散格式．并利用Sobolev空间的正交映射理论,给出了这两种格式的误差估计．最后针对全离散格式给出了数值算例,数值结果表明Fourier伪谱格式能正确加解密,且计算误差较小,效率较高,具有较好的稳定性,可用于提高热流密码体制的加解密效率．
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| 关 键 词： | 伪抛物型方程 非线性 Fburier伪谱方法 误差估计 数值模拟 |
| 修稿时间： | 2006-01-21 |
PSEUDOSPECTRAL METHODS FOR SOME NONLINEAR PSEUDO-PARABOLIC EQUATION |
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| Liu Linwen,Liu Chao,Jiang Chengshun.PSEUDOSPECTRAL METHODS FOR SOME NONLINEAR PSEUDO-PARABOLIC EQUATION[J].Mathematica Numerica Sinica,2007,29(1):99-12. |
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| Authors: | Liu Linwen Liu Chao Jiang Chengshun |
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| Institution: | Institute of Information Engineering, Information Engineering University, Zhengzhou 450002, China;Institute of Information Engineering, Information Engineering University, Zhengzhou 450002, China; State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 210023, Liaoning, China |
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| Abstract: | In this paper, some nonlinear pseudoparabolic equation is considered. The semidiscrete and fully discrete pseudospectral schemes are constructed. The error estimations of these two schemes are obtained by using the theory of orthogonal mapping of ploynomials in Sobolev spaces. The numerical simulations of the fully discrete scheme are also provided. The numerical results show that the Fourier pseudospectral schemes are robust and efficient. They are suitable for improving the efficiency of encryption and decryption. |
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| Keywords: | pseudo-parabolic functions nonlinear Fourier pseudospectral method error estimations numerical simulation |
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