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

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

2006-02-07

arxiv.org/abs/cs/0602025v1

Computer Science

Numerical Analysis

12 pages, 2 figures; keywords: ordinary differential equations, implicit function theorem, local solutions, symbolic solutions

Scientific paper

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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