Fuzzy transform algorithm based on high-resolution compact discretization for three-dimensional nonlinear elliptic PDEs and convection–diffusion equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402N4T" target="_blank" >RIV/61988987:17610/23:A2402N4T - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00500-023-09146-0#citeas" target="_blank" >https://link.springer.com/article/10.1007/s00500-023-09146-0#citeas</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-023-09146-0" target="_blank" >10.1007/s00500-023-09146-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Fuzzy transform algorithm based on high-resolution compact discretization for three-dimensional nonlinear elliptic PDEs and convection–diffusion equations

Popis výsledku v původním jazyce

This paper deals with a high-resolution algorithm that engages fuzzy transform to solve three-dimensional nonlinear elliptic partial differential equations. The scheme approximates the fuzzy components, which estimate fourth-order accurate solutions at the interior mesh points of the solution domain. The fuzzy components and triangular base functions will be approximated with a nineteen-point linear combination of solution values and related to exact solutions by a linear system. Such an arrangement along with compact discretization yields a block tridiagonal Jacobian matrix, and an iterative solver can efficiently compute them. The convergence analysis and error bound of the scheme are examined in detail. The method provides an order-preserving solution and applies to a comprehensive class of partial differential equations with nonlinear first-order partial derivatives. Numerical simulations with Helmholtz equation, advection–diffusion–reaction equation, and nonlinear elliptic sine–Gordan equation corroborate the utility, convergence rate, and enhance solution accuracy by employing a new scheme.

Název v anglickém jazyce

Fuzzy transform algorithm based on high-resolution compact discretization for three-dimensional nonlinear elliptic PDEs and convection–diffusion equations

Popis výsledku anglicky

This paper deals with a high-resolution algorithm that engages fuzzy transform to solve three-dimensional nonlinear elliptic partial differential equations. The scheme approximates the fuzzy components, which estimate fourth-order accurate solutions at the interior mesh points of the solution domain. The fuzzy components and triangular base functions will be approximated with a nineteen-point linear combination of solution values and related to exact solutions by a linear system. Such an arrangement along with compact discretization yields a block tridiagonal Jacobian matrix, and an iterative solver can efficiently compute them. The convergence analysis and error bound of the scheme are examined in detail. The method provides an order-preserving solution and applies to a comprehensive class of partial differential equations with nonlinear first-order partial derivatives. Numerical simulations with Helmholtz equation, advection–diffusion–reaction equation, and nonlinear elliptic sine–Gordan equation corroborate the utility, convergence rate, and enhance solution accuracy by employing a new scheme.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Soft Computing

ISSN

1432-7643

e-ISSN

1433-7479

Svazek periodika

—

Číslo periodika v rámci svazku

28.09.2023

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

26

Strana od-do

17525-17550

Kód UT WoS článku

001074767600006

EID výsledku v databázi Scopus

2-s2.0-85173033108