An Integral Equation Method for Linear Two-Point Boundary Value Systems

Fuente: arXiv
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Hauptverfasser: Zhang, Tianze, Ma, Yixuan, Wang, Jun
Format: Preprint
Veröffentlicht: 2025
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author Zhang, Tianze
Ma, Yixuan
Wang, Jun
author_facet Zhang, Tianze
Ma, Yixuan
Wang, Jun
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_06678
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An Integral Equation Method for Linear Two-Point Boundary Value Systems
Zhang, Tianze
Ma, Yixuan
Wang, Jun
Numerical Analysis
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.
title An Integral Equation Method for Linear Two-Point Boundary Value Systems
topic Numerical Analysis
url https://arxiv.org/abs/2510.06678