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.
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