Numerical solutions of ordinary differential equations using Spline-Integral Operator

2024/09/30 by Gustavo H. O. Salgado, Salgado, Gustavo H. O., João P. R. Romanelli +1
Mathematics · #65L05 #65L07 #Applied mathematics #Differential Equations and Numerical Methods #Differential equation #FOS: Mathematics #Fourier integral operator #Fractional Differential Equations Solutions #Integral equation #Iterative Methods for Nonlinear Equations #Mathematical analysis #Mathematics #Numerical Analysis (math.NA) #Operator (biology) #Ordinary differential equation #Physics #Spline (mechanical)

paper · pdf · doi:10.48550/arxiv.2409.20369

openalex publication_date 2024/09/30 · openalex created_date 2024/10/28 · openalex updated_date 2026/07/28

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.

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