On local symbolic approximation and resolution of ODEs using Implicit Function Theorem

2006/02/07 by Gianluca Argentini, Argentini, Gianluca
Computer Science · Engineering · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #G.1.7 #Heat Transfer and Optimization #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.cs/0602025

openalex publication_date 2006/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work the implicit function theorem is used for searching local symbolic resolution of differential equations. General results of existence for first order equations are proven and some examples, one relative to cavitation in a fluid, are developed. These examples seem to show that local approximation of non linear differential equations can give useful informations about symbolic form of possible solutions, and in the case a global solution is known, locally the accuracy of approximation can be good.

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