PreprintCC BY 4.0arXiv
A Christov Integrating Factor Method for Approximating Rational PDE Solutions
Abstract
Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a basis of orthogonal functions known as the Christov functions, allowing for the computation of its spectrum via the fast Fourier transform. An explicit fourth-order integrating factor method is derived. The effectiveness of the method is tested on several nonlinear PDEs. Relative to a straightforward pseudo-spectral approximation, the integrating factor method supports larger regions of stability resulting in a more efficient scheme.
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BibTeX
@misc{johnson2026christov,
title = {{A Christov Integrating Factor Method for Approximating Rational PDE Solutions}},
author = {Troy I. Johnson and Justin T. Cole},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07154},
eprint = {2611.07154},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07154},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Christov Integrating Factor Method for Approximating Rational PDE Solutions
AU - Troy I. Johnson
AU - Justin T. Cole
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07154
UR - https://arxiv.org/abs/2611.07154
AB - Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a basis of orthogonal functions known as the Christov functions, allowing for the computation of its spectrum via the fast Fourier transform. An explicit fourth-order integrating factor method is derived. The effectiveness of the method is tested on several nonlinear PDEs. Relative to a straightforward pseudo-spectral approximation, the integrating factor method supports larger regions of stability resulting in a more efficient scheme.
ER -