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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Name of the periodical

MethodsX

ISSN

2215-0161

e-ISSN

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Volume of the periodical

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Issue of the periodical within the volume

26.04.2023

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

31

Pages from-to

1-31

UT code for WoS article

001053178900001

EID of the result in the Scopus database

2-s2.0-85156233607