A high-resolution fuzzy transform combined compact scheme for 2D nonlinear elliptic partial differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402I44" target="_blank" >RIV/61988987:17610/23:A2402I44 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S2215016123002029" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2215016123002029</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.mex.2023.102206" target="_blank" >10.1016/j.mex.2023.102206</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A high-resolution fuzzy transform combined compact scheme for 2D nonlinear elliptic partial differential equations

Popis výsledku v původním jazyce

This paper proposes a new high-resolution fuzzy transform algorithm for solving two-dimensional nonlinear elliptic partial differential equations (PDEs). The underlying new computational method implements the method of so-called approximating fuzzy components, which evaluate the solution values with fourth-order accuracy at internal mesh points. Triangular basic functions and fuzzy components are locally determined by linear combinations of solution values at nine points. Such a scheme connects the proposed method of approximating fuzzy components with the exact values of the solution using a linear system of equations. Compact approximations of high-resolution fuzzy components using nine points give a block tridiagonal Jacobi matrix. Apart from the numerical solution, it is easy to construct closed-form approximate solutions using a 2D spline interpolation polynomial from the available data with fuzzy components. The upper bounds of the approximation errors are estimated, as well as the convergence of the approximating solutions. Simulations with linear and nonlinear elliptical PDEs arising from quantum mechanics and convection-dominated diffusion phenomena are presented to confirm the usefulness of the new scheme and fourth-order convergence. To summarize:•The paper presents a high-resolution numerical method for the two-dimensions elliptic PDEs with nonlinear terms.•The combined effect of fuzzy transform and compact discretizations yields almost fourth-order accuracies to Schrodinger equation, convection-diffusion equation, and Burgers equation.•The high-order numerical scheme is computationally efficient and employs minimal data storage.

Název v anglickém jazyce

A high-resolution fuzzy transform combined compact scheme for 2D nonlinear elliptic partial differential equations

Popis výsledku anglicky

This paper proposes a new high-resolution fuzzy transform algorithm for solving two-dimensional nonlinear elliptic partial differential equations (PDEs). The underlying new computational method implements the method of so-called approximating fuzzy components, which evaluate the solution values with fourth-order accuracy at internal mesh points. Triangular basic functions and fuzzy components are locally determined by linear combinations of solution values at nine points. Such a scheme connects the proposed method of approximating fuzzy components with the exact values of the solution using a linear system of equations. Compact approximations of high-resolution fuzzy components using nine points give a block tridiagonal Jacobi matrix. Apart from the numerical solution, it is easy to construct closed-form approximate solutions using a 2D spline interpolation polynomial from the available data with fuzzy components. The upper bounds of the approximation errors are estimated, as well as the convergence of the approximating solutions. Simulations with linear and nonlinear elliptical PDEs arising from quantum mechanics and convection-dominated diffusion phenomena are presented to confirm the usefulness of the new scheme and fourth-order convergence. To summarize:•The paper presents a high-resolution numerical method for the two-dimensions elliptic PDEs with nonlinear terms.•The combined effect of fuzzy transform and compact discretizations yields almost fourth-order accuracies to Schrodinger equation, convection-diffusion equation, and Burgers equation.•The high-order numerical scheme is computationally efficient and employs minimal data storage.

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

2023

Kód důvěrnosti údajů

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

Název periodika

MethodsX

ISSN

2215-0161

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

26.04.2023

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

31

Strana od-do

1-31

Kód UT WoS článku

001053178900001

EID výsledku v databázi Scopus

2-s2.0-85156233607