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Mathematics
Volume 13
Issue 11
10.3390/math13111719
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Article

Error Estimate for a Finite-Difference Crank–Nicolson–ADI Scheme for a Class of Nonlinear Parabolic Isotropic Systems

by
Chrysovalantis A. Sfyrakis
† and
Markos Tsoukalas
*,†
Department of Mechanical Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Station “Eirini HSAP”, 15122 Marousi, Greece
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2025, 13(11), 1719; https://doi.org/10.3390/math13111719
Submission received: 27 February 2025 / Revised: 21 May 2025 / Accepted: 22 May 2025 / Published: 23 May 2025
(This article belongs to the Topic Numerical Methods for Partial Differential Equations)
Review Reports Versions Notes

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 phase-field model; finite-difference method; Crank–Nicolson scheme; ADI method; error estimate; nonlinear parabolic system

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MDPI and ACS Style

Sfyrakis, C.A.; Tsoukalas, M. Error Estimate for a Finite-Difference Crank–Nicolson–ADI Scheme for a Class of Nonlinear Parabolic Isotropic Systems. Mathematics 2025, 13, 1719. https://doi.org/10.3390/math13111719

AMA Style

Sfyrakis CA, Tsoukalas M. Error Estimate for a Finite-Difference Crank–Nicolson–ADI Scheme for a Class of Nonlinear Parabolic Isotropic Systems. Mathematics. 2025; 13(11):1719. https://doi.org/10.3390/math13111719

Chicago/Turabian Style

Sfyrakis, Chrysovalantis A., and Markos Tsoukalas. 2025. "Error Estimate for a Finite-Difference Crank–Nicolson–ADI Scheme for a Class of Nonlinear Parabolic Isotropic Systems" Mathematics 13, no. 11: 1719. https://doi.org/10.3390/math13111719

APA Style

Sfyrakis, C. A., & Tsoukalas, M. (2025). Error Estimate for a Finite-Difference Crank–Nicolson–ADI Scheme for a Class of Nonlinear Parabolic Isotropic Systems. Mathematics, 13(11), 1719. https://doi.org/10.3390/math13111719

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