An Integral Equation Method for Linear Two-Point Boundary Value Systems
Numerical Analysis
2025-10-09 v1 Numerical Analysis
Abstract
We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a well-conditioned integral equation. We then make use of a high-order Nystrom discretization and a fast direct solver on the continuous level to obtain a black-box solver that is fast and accurate. A numerical study of the conditioning of different integral formulations is carried out. Excellent performance in speed, accuracy, and robustness is demonstrated with several challenging numerical examples.
Cite
@article{arxiv.2510.06678,
title = {An Integral Equation Method for Linear Two-Point Boundary Value Systems},
author = {Tianze Zhang and Yixuan Ma and Jun Wang},
journal= {arXiv preprint arXiv:2510.06678},
year = {2025}
}