Differential Equations as a Projection of Implicit Functions Using Spatio-Temporal Taylor Expansion and Critical Points Properties

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F24%3A43976634" target="_blank" >RIV/49777513:23520/24:43976634 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1063/5.0210444" target="_blank" >https://doi.org/10.1063/5.0210444</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0210444" target="_blank" >10.1063/5.0210444</a>

Result language

angličtina

Original language name

Differential Equations as a Projection of Implicit Functions Using Spatio-Temporal Taylor Expansion and Critical Points Properties

Original language description

This contribution introduces a novel method for formulating differential equations. This method relies on expanding an implicit function that varies with time (denoted as &quot;t&quot;) in the space-time domain using Taylor series. This formulation encompasses both ordinary differential equations (ODEs) and partial differential equations (PDEs).In the context of visualizing vector fields, such as fluid flow and electromagnetic fields, the critical points of ODEs play a crucial role in understanding physical phenomena behavior. This paper outlines a general approach for formulating ODEs and PDEs by treating them as time-varying scalar functions using the Taylor expansion. Furthermore, a new condition for identifying critical points is derived and specified specifically for cases where the function is invariant with respect to time (referred to as &quot;t-invariant&quot;). This newly derived formula enhances the detection of critical points, particularly in the context of acquiring and analyzing large 3D fluid flow data. This advancement enables efficient compression of 3D vector data and their representation through radial basis functions (RBFs).

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

AIP Conference Proceedings

ISBN

978-0-7354-4954-1

ISSN

0094-243X

e-ISSN

1551-7616

Number of pages

4

Pages from-to

1-4

Publisher name

AIP Publishing

Place of publication

Heraklion

Event location

Heraklion

Event date

Sep 19, 2022

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

001244923000099