Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system in optical applications
Numerical Analysis
2020-11-24 v1 Numerical Analysis
Abstract
Based on the generalized Cayley transform, a family of conservative one-step schemes of the sixth order of accuracy for the Zakharov-Shabat system is constructed. The exponential integrator is a special case. Schemes based on rational approximation allow the use of fast algorithms to solve the initial problem for a large number of values of the spectral parameter.
Cite
@article{arxiv.2011.11380,
title = {Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system in optical applications},
author = {Sergey Medvedev and Igor Chekhovskoy and Irina Vaseva and Mikhail Fedoruk},
journal= {arXiv preprint arXiv:2011.11380},
year = {2020}
}