Spectral analysis and sine transform based preconditioning for a structure preserving stabilized scheme approximating the space-fractional Allen Cahn equation with logarithmic potential
Numerical Analysis
2026-05-27 v2 Numerical Analysis
Abstract
We consider an initial boundary value problem of the space fractional Allen-Cahn equation with logarithmic Flory-Huggins potential. As an approximation technique, first-order weighted and shifted Grunwald difference formulae of the left and right fractional derivatives are used. The main focus of the present work is to study the spectral features of the underlying matrices and matrix sequences and to design proper preconditioners based on the spectral information. Then a computational and spectral analysis of the resulting preconditioned matrix sequences is performed. Numerical evidence and a short list of open problems complete the current study.
Keywords
Cite
@article{arxiv.2605.24387,
title = {Spectral analysis and sine transform based preconditioning for a structure preserving stabilized scheme approximating the space-fractional Allen Cahn equation with logarithmic potential},
author = {Danyal Ahmad and Stefano Serra-Capizzano and Muhammad Sohaib and Cristina Tablino-Possio},
journal= {arXiv preprint arXiv:2605.24387},
year = {2026}
}