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

Chrysovalantis A. Sfyrakis and Markos Tsoukalas ()
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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
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