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

Yahia Awad (), Hussein Fakih and Yousuf Alkhezi
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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
Yousuf Alkhezi: Mathematics Department, College of Basic Education, Public Authority for Applied Education and Training (PAAET), P.O. Box 34053, Kuwait City 70654, Kuwait

Mathematics, 2023, vol. 11, issue 24, 1-31

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.

Keywords: Cahn–Hilliard equation; image inpainting; finite difference method; numerical linear algebra; stability; steady state (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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