F-transform utility in the operational-matrix approach to the Volterra integral equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F24%3AA2502MI8" target="_blank" >RIV/61988987:17610/24:A2502MI8 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/abs/pii/S0165011423004098?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0165011423004098?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2023.108764" target="_blank" >10.1016/j.fss.2023.108764</a>

Jazyk výsledku

angličtina

Název v původním jazyce

F-transform utility in the operational-matrix approach to the Volterra integral equation

Popis výsledku v původním jazyce

The proposed approach, based on the F-transform, consists in constructing an operational matrix for the Volterra integral equation as a Hadamard product of two matrices, one of which refers to the Volterra operator, and the other to its kernel. As a result, the F-transformed form of the entire equation reduces to a system of linear equations with a triangular matrix. This makes the corresponding numerical method for solving the Volterra integral equation efficient and low computational. We provide all the necessary proofs of the supporting statements, including the convergence of the method, and estimate its computational complexity. Finally, we illustrate the proposed algorithm with test cases and compare their results with some recently published methods.

Název v anglickém jazyce

F-transform utility in the operational-matrix approach to the Volterra integral equation

Popis výsledku anglicky

The proposed approach, based on the F-transform, consists in constructing an operational matrix for the Volterra integral equation as a Hadamard product of two matrices, one of which refers to the Volterra operator, and the other to its kernel. As a result, the F-transformed form of the entire equation reduces to a system of linear equations with a triangular matrix. This makes the corresponding numerical method for solving the Volterra integral equation efficient and low computational. We provide all the necessary proofs of the supporting statements, including the convergence of the method, and estimate its computational complexity. Finally, we illustrate the proposed algorithm with test cases and compare their results with some recently published methods.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centrum pro výzkum a vývoj metod umělé intelligence v automobilovém průmyslu regionu</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

1872-6801

Svazek periodika

—

Číslo periodika v rámci svazku

15.1.2024

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

31

Strana od-do

1-31

Kód UT WoS článku

001110974300001

EID výsledku v databázi Scopus

2-s2.0-85175795100