Order-preserving fuzzy transform for singular boundary value problems of polytropic gas flow and sewage diffusion

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F24%3AA2502N4W" target="_blank" >RIV/61988987:17610/24:A2502N4W - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/abs/pii/S0165011423003937" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0165011423003937</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2023.108748" target="_blank" >10.1016/j.fss.2023.108748</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Order-preserving fuzzy transform for singular boundary value problems of polytropic gas flow and sewage diffusion

Popis výsledku v původním jazyce

We describe a fuzzy transform method to analyze two-point singular and non-singular boundary value problems with high-order solution accuracies. This framework implements a fuzzy transform that approximates solutions with fourth-order accuracy at the interior mesh points. The fuzzy components and the triangular base function are locally arranged with a three-point linear combination of solution values. This yields a tri-diagonal Jacobian matrix that can be easily computed in a space-time efficient manner. Since a linear system relates solution values and fuzzy components, it is easy to obtain solution approximations via fuzzy components by a tri-diagonal matrix inversion. In addition to the numerical solution, it is easy to determine an approximate analytic solution using a cubic spline interpolating polynomial from the data available with fuzzy components. The error estimates for approximate analytical solutions and numerical solutions are obtained by integrated absolute error and maximum absolute errors. The new mechanism is analyzed for convergence using matrix theory. Several linear and nonlinear equations of practical importance related to sewage diffusion and polytropic gas flow models are simulated to corroborate the new scheme’s utility and fourth-order convergence.

Název v anglickém jazyce

Order-preserving fuzzy transform for singular boundary value problems of polytropic gas flow and sewage diffusion

Popis výsledku anglicky

We describe a fuzzy transform method to analyze two-point singular and non-singular boundary value problems with high-order solution accuracies. This framework implements a fuzzy transform that approximates solutions with fourth-order accuracy at the interior mesh points. The fuzzy components and the triangular base function are locally arranged with a three-point linear combination of solution values. This yields a tri-diagonal Jacobian matrix that can be easily computed in a space-time efficient manner. Since a linear system relates solution values and fuzzy components, it is easy to obtain solution approximations via fuzzy components by a tri-diagonal matrix inversion. In addition to the numerical solution, it is easy to determine an approximate analytic solution using a cubic spline interpolating polynomial from the data available with fuzzy components. The error estimates for approximate analytical solutions and numerical solutions are obtained by integrated absolute error and maximum absolute errors. The new mechanism is analyzed for convergence using matrix theory. Several linear and nonlinear equations of practical importance related to sewage diffusion and polytropic gas flow models are simulated to corroborate the new scheme’s utility and fourth-order convergence.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

FUZZY SET SYST

ISSN

0165-0114

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

15.01.2024

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

19

Strana od-do

1-19

Kód UT WoS článku

001102124500001

EID výsledku v databázi Scopus

2-s2.0-85174802940