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Numerical Linear Algebra for the Two-Dimensional Bertozzi–Esedoglu–Gillette–Cahn–Hilliard Equation in Image Inpainting

Author

Listed:
  • Yahia Awad

    (Department of Mathematics and Physics, Bekaa Campus, Lebanese International University (LIU), Al-Khyara P.O. Box 5, Lebanon)

  • Hussein Fakih

    (Department of Mathematics and Physics, Bekaa Campus, Lebanese International University (LIU), Al-Khyara P.O. Box 5, Lebanon
    Department of Mathematics and Physics, Beirut Campus, The International University of Beirut (BIU), Beirut P.O. Box 1001, Lebanon
    Khawarizmi Laboratory for Mathematics and Applications, Department of Mathematics, Lebanese University, Beirut P.O. Box 1001, Lebanon)

  • Yousuf Alkhezi

    (Mathematics Department, College of Basic Education, Public Authority for Applied Education and Training (PAAET), P.O. Box 34053, Kuwait City 70654, Kuwait)

Abstract

In this paper, we present a numerical linear algebra analytical study of some schemes for the Bertozzi–Esedoglu–Gillette–Cahn–Hilliard equation. Both 1D and 2D finite difference discretizations in space are proposed with semi-implicit and implicit discretizations on time. We prove that our proposed numerical solutions converge to continuous solutions.

Suggested Citation

  • Yahia Awad & Hussein Fakih & Yousuf Alkhezi, 2023. "Numerical Linear Algebra for the Two-Dimensional Bertozzi–Esedoglu–Gillette–Cahn–Hilliard Equation in Image Inpainting," Mathematics, MDPI, vol. 11(24), pages 1-31, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4952-:d:1300110
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