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

Zhong-qing Wang & Ben-yu Guo

DOI:

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 solu- tion 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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@Article{JCM-22-457, author = {}, 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 solu- tion 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 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 KW - The whole line KW - 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 solu- tion 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.
Zhong-qing Wang & Ben-yu Guo. (1970). Modified Legendre Rational Spectral Method for the Whole Line. Journal of Computational Mathematics. 22 (3). 457-474. doi:
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