The Lipschitz K(t) – Function for the Initial Value Problem (i.v.p) of an Ordinary Differential Equation (o.d.e) in One Dimension

An elaborate but brief proof of the existence and uniqueness of the solution of an i.v.p for an o.d.e. is given. Because in both proofs the same initial condition is used, a considerable simplification of the K(t) Lipschitz function takes place. If the solution of the o.d.e. is known then the maximum interval of existence of the o.d.e. can be found again.

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Publication Details

Journal
European journal of applied sciences
Published
2025-05-09
DOI
https://doi.org/10.14738/aivp.1303.18776
Primary Topic
Numerical methods for differential equations
Type
article
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article

The Lipschitz K(t) – Function for the Initial Value Problem (i.v.p) of an Ordinary Differential Equation (o.d.e) in One Dimension

Thanassis Dialynas
1 links
European journal of applied sciences
Numerical methods for differential equations
article

The Lipschitz K(t) – Function for the Initial Value Problem (i.v.p) of an Ordinary Differential Equation (o.d.e) in One Dimension

Thanassis Dialynas
article en

Abstract

An elaborate but brief proof of the existence and uniqueness of the solution of an i.v.p for an o.d.e. is given. Because in both proofs the same initial condition is used, a considerable simplification of the K(t) Lipschitz function takes place. If the solution of the o.d.e. is known then the maximum interval of existence of the o.d.e. can be found again.

European journal of applied sciencesVol. 13(03)
University of Crete (GR)
Openalex Percentile: Top 82%
Numerical methods for differential equations
DOIOpen Access PDFOpenAlex
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The Lipschitz K(t) – Function for the Initial Value Problem (i.v.p) of an Ordinary Differential Equation (o.d.e) in One Dimension — Thanassis Dialynas · European journal of applied sciences (2025) | TGRS Research Map | TGRS