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Volume 22, Issue 3
Modified Legendre Rational Spectral Method for the Whole Line

Zhongqing Wang & Benyu Guo

J. Comp. Math., 22 (2004), pp. 457-474.

Published online: 2004-06

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  • Abstract

A mutually orthogonal system of rational functions on the whole line is introduced. Some approximation results are established. As an example of applications, a modified Legendre rational spectral scheme is given for the Dirac equation. Its numerical solution keeps the same conservation as the genuine solution. This feature not only leads to reasonable numerical simulation of nonlinear waves, but also simplifies the analysis. The convergence of the proposed scheme is proved. Numerical results demonstrate the efficiency of this new approach and coincide with the analysis well.

  • Keywords

Modified Legendre rational approximation, The whole line, Dirac equation.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-457, author = {Wang , Zhongqing and Guo , Benyu}, title = {Modified Legendre Rational Spectral Method for the Whole Line}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {3}, pages = {457--474}, abstract = {

A mutually orthogonal system of rational functions on the whole line is introduced. Some approximation results are established. As an example of applications, a modified Legendre rational spectral scheme is given for the Dirac equation. Its numerical solution keeps the same conservation as the genuine solution. This feature not only leads to reasonable numerical simulation of nonlinear waves, but also simplifies the analysis. The convergence of the proposed scheme is proved. Numerical results demonstrate the efficiency of this new approach and coincide with the analysis well.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10319.html} }
TY - JOUR T1 - Modified Legendre Rational Spectral Method for the Whole Line AU - Wang , Zhongqing AU - Guo , Benyu JO - Journal of Computational Mathematics VL - 3 SP - 457 EP - 474 PY - 2004 DA - 2004/06 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10319.html KW - Modified Legendre rational approximation, The whole line, Dirac equation. AB -

A mutually orthogonal system of rational functions on the whole line is introduced. Some approximation results are established. As an example of applications, a modified Legendre rational spectral scheme is given for the Dirac equation. Its numerical solution keeps the same conservation as the genuine solution. This feature not only leads to reasonable numerical simulation of nonlinear waves, but also simplifies the analysis. The convergence of the proposed scheme is proved. Numerical results demonstrate the efficiency of this new approach and coincide with the analysis well.

Wang , Zhongqing and Guo , Benyu. (2004). Modified Legendre Rational Spectral Method for the Whole Line. Journal of Computational Mathematics. 22 (3). 457-474. doi:
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