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一类非线性伪抛物型方程的伪谱解法

刘霖雯,刘超,江成顺,   

  1. 信息工程大学信息工程学院,信息工程大学信息工程学院,信息工程大学信息工程学院 郑州 450002,郑州 450002 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,郑州 450002 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
  • 出版日期:2007-01-14 发布日期:2007-01-14

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.

PSEUDOSPECTRAL METHODS FOR SOME NONLINEAR PSEUDO-PARABOLIC EQUATION

  1. Liu Linwen (Institute of Information Engineering, Information Engineering University, Zhengzhou 450002, China) Liu Chao Jiang Chengshun (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)
  • Online:2007-01-14 Published:2007-01-14
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.
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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