On the Numerical Solution of Ordinary, Interval and Fuzzy Differential Equations by Use of F-Transform

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F20%3A10245356" target="_blank" >RIV/61989100:27510/20:10245356 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.scopus.com/record/display.uri?eid=2-s2.0-85081556271&origin=resultslist&sort=plf-f&src=s&st1=radi%2c+d&st2=&sid=b5e7922457e298202b1fb3eaf34f31d6&sot=b&sdt=b&sl=20&s=AUTHOR-NAME%28radi%2c+d%29&relpos=4&citeCnt=0&searchTerm=" target="_blank" >https://www.scopus.com/record/display.uri?eid=2-s2.0-85081556271&origin=resultslist&sort=plf-f&src=s&st1=radi%2c+d&st2=&sid=b5e7922457e298202b1fb3eaf34f31d6&sot=b&sdt=b&sl=20&s=AUTHOR-NAME%28radi%2c+d%29&relpos=4&citeCnt=0&searchTerm=</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/axioms9010015" target="_blank" >10.3390/axioms9010015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Numerical Solution of Ordinary, Interval and Fuzzy Differential Equations by Use of F-Transform

Popis výsledku v původním jazyce

An interesting property of the inverse F-transform f&lt;^&gt; of a continuous function f on a given interval [a,b] says that the integrals of f&lt;^&gt; and f on [a,b] coincide. Furthermore, the same property can be established for the restrictions of the functions to all subintervals [a,pk] of the fuzzy partition of [a,b] used to define the F-transform. Based on this fact, we propose a new method for the numerical solution of ordinary differential equations (initial-value ordinary differential equation (ODE)) obtained by approximating the derivative x center dot(t) via F-transform, then computing (an approximation of) the solution x(t) by exact integration. For an ODE, a global second-order approximation is obtained. A similar construction is then applied to interval-valued and (level-wise) fuzzy differential equations in the setting of generalized differentiability (gH-derivative). Properties of the new method are analyzed and a computational section illustrates the performance of the obtained procedures, in comparison with well-known efficient algorithms.

Název v anglickém jazyce

On the Numerical Solution of Ordinary, Interval and Fuzzy Differential Equations by Use of F-Transform

Popis výsledku anglicky

An interesting property of the inverse F-transform f&lt;^&gt; of a continuous function f on a given interval [a,b] says that the integrals of f&lt;^&gt; and f on [a,b] coincide. Furthermore, the same property can be established for the restrictions of the functions to all subintervals [a,pk] of the fuzzy partition of [a,b] used to define the F-transform. Based on this fact, we propose a new method for the numerical solution of ordinary differential equations (initial-value ordinary differential equation (ODE)) obtained by approximating the derivative x center dot(t) via F-transform, then computing (an approximation of) the solution x(t) by exact integration. For an ODE, a global second-order approximation is obtained. A similar construction is then applied to interval-valued and (level-wise) fuzzy differential equations in the setting of generalized differentiability (gH-derivative). Properties of the new method are analyzed and a computational section illustrates the performance of the obtained procedures, in comparison with well-known efficient algorithms.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50200 - Economics and Business

Projekt

<a href="/cs/project/GA20-16701S" target="_blank" >GA20-16701S: Hybridní evoluční hry a ekonomické aplikace</a><br>

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Axioms

ISSN

2075-1680

e-ISSN

—

Svazek periodika

9

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

37

Strana od-do

15

Kód UT WoS článku

000523486100032

EID výsledku v databázi Scopus

2-s2.0-85081556271