Error Estimate for a Finite-Difference Crank–Nicolson–ADI Scheme for a Class of Nonlinear Parabolic Isotropic Systems
Chrysovalantis A. Sfyrakis and
Markos Tsoukalas ()
Additional contact information
Chrysovalantis A. Sfyrakis: Department of Mechanical Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Station “Eirini HSAP”, 15122 Marousi, Greece
Markos Tsoukalas: Department of Mechanical Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Station “Eirini HSAP”, 15122 Marousi, Greece
Mathematics, 2025, vol. 13, issue 11, 1-18
Abstract:
To understand phase-transition processes like solidification, phase-field models are frequently employed. In this paper, we study a finite-difference Crank–Nicolson–ADI scheme for a class of nonlinear parabolic isotropic systems. We establish an error estimate for this scheme, demonstrating its effectiveness in solving phase-field models. Our analysis provides rigorous mathematical justification for the numerical method’s reliability in simulating phase transitions.
Keywords: phase-field model; finite-difference method; Crank–Nicolson scheme; ADI method; error estimate; nonlinear parabolic system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:
Downloads: (external link)
https://www.mdpi.com/2227-7390/13/11/1719/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/11/1719/ (text/html)
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:11:p:1719-:d:1662973
Access Statistics for this article
Mathematics is currently edited by Ms. Emma He
More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().