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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Fuzzy transform algorithm based on high-resolution compact discretization for three-dimensional nonlinear elliptic PDEs and convection–diffusion equations
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied 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

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