Volume 16, Issue 4
High Order Pade Schemes for Nonlinear Wave Propagation Problems

P. L. Li & R. X. Liu

DOI:

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 370-382

Published online: 2007-11

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  • Abstract

Split-step Pad\'{e} method and split-step fourier method are applied to the higher-order nonlinear Schr\"{o}dinger equation. It is proved that a combination of Pad\'{e} scheme and spectral method is the most effective method, which has a spectral-like resolution and good stability nature. In particular, we propose an unconditional stable implicit Pad\'{e} scheme to solve odd order nonlinear equations. Numerical results demonstrate the excellent performance of Pad\'{e} schemes for high order nonlinear equations.

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@Article{NM-16-370, author = {P. L. Li and R. X. Liu}, title = {High Order Pade Schemes for Nonlinear Wave Propagation Problems}, journal = {Numerical Mathematics, a Journal of Chinese Uniersities}, year = {2007}, volume = {16}, number = {4}, pages = {370--382}, abstract = { Split-step Pad\'{e} method and split-step fourier method are applied to the higher-order nonlinear Schr\"{o}dinger equation. It is proved that a combination of Pad\'{e} scheme and spectral method is the most effective method, which has a spectral-like resolution and good stability nature. In particular, we propose an unconditional stable implicit Pad\'{e} scheme to solve odd order nonlinear equations. Numerical results demonstrate the excellent performance of Pad\'{e} schemes for high order nonlinear equations.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/10066.html} }
TY - JOUR T1 - High Order Pade Schemes for Nonlinear Wave Propagation Problems AU - P. L. Li & R. X. Liu JO - Numerical Mathematics, a Journal of Chinese Uniersities VL - 4 SP - 370 EP - 382 PY - 2007 DA - 2007/11 SN - 16 DO - http://dor.org/ UR - https://global-sci.org/intro/nm/10066.html KW - AB - Split-step Pad\'{e} method and split-step fourier method are applied to the higher-order nonlinear Schr\"{o}dinger equation. It is proved that a combination of Pad\'{e} scheme and spectral method is the most effective method, which has a spectral-like resolution and good stability nature. In particular, we propose an unconditional stable implicit Pad\'{e} scheme to solve odd order nonlinear equations. Numerical results demonstrate the excellent performance of Pad\'{e} schemes for high order nonlinear equations.
P. L. Li & R. X. Liu. (1970). High Order Pade Schemes for Nonlinear Wave Propagation Problems. Numerical Mathematics, a Journal of Chinese Uniersities. 16 (4). 370-382. doi:
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