Solving nonlinear ODEs with the ultraspherical spectral method
Numerical Analysis
2023-07-03 v1 Numerical Analysis
Abstract
We extend the ultraspherical spectral method to solving nonlinear ODE boundary value problems. We propose to use the inexact Newton-GMRES framework for which an effective preconditioner can be constructed and a fast Jacobian-vector multiplication can be effected, thanks to the structured operators of the ultraspherical spectral method. With a mixed-precision implementation, the inexact Newton-GMRES-ultraspherical framework exhibits extraordinary speed and accuracy, as we show by extensive numerical experiments.
Cite
@article{arxiv.2306.17688,
title = {Solving nonlinear ODEs with the ultraspherical spectral method},
author = {Ouyuan Qin and Kuan Xu},
journal= {arXiv preprint arXiv:2306.17688},
year = {2023}
}
Comments
23 pages, 4 figures