English

Numerical solutions of ordinary differential equations using Spline-Integral Operator

Numerical Analysis 2024-10-01 v1 Numerical Analysis

Abstract

In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the analytical solution. Furthermore, we offer a rigorous proof of the method's order and provide a comprehensive stability analysis. Additionally, we showcase the effectiveness method through some examples, comparing with Taylor's methods of same order.

Keywords

Cite

@article{arxiv.2409.20369,
  title  = {Numerical solutions of ordinary differential equations using Spline-Integral Operator},
  author = {Gustavo H. O. Salgado and João P. R. Romanelli},
  journal= {arXiv preprint arXiv:2409.20369},
  year   = {2024}
}

Comments

13 pages, 5 figures

R2 v1 2026-06-28T19:02:26.486Z