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

Author

Listed:
  • Chrysovalantis A. Sfyrakis

    (Department of Mechanical Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Station “Eirini HSAP”, 15122 Marousi, Greece
    These authors contributed equally to this work.)

  • Markos Tsoukalas

    (Department of Mechanical Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Station “Eirini HSAP”, 15122 Marousi, Greece
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Chrysovalantis A. Sfyrakis & Markos Tsoukalas, 2025. "Error Estimate for a Finite-Difference Crank–Nicolson–ADI Scheme for a Class of Nonlinear Parabolic Isotropic Systems," Mathematics, MDPI, vol. 13(11), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1719-:d:1662973
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