@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 Universities}, 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} }