Spectral analysis and sine transform based preconditioning for a structure preserving stabilized scheme approximating the space-fractional Allen Cahn equation with logarithmic potential
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917532889251840 |
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| author | Ahmad, Danyal Serra-Capizzano, Stefano Sohaib, Muhammad Tablino-Possio, Cristina |
| author_facet | Ahmad, Danyal Serra-Capizzano, Stefano Sohaib, Muhammad Tablino-Possio, Cristina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24387 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral analysis and sine transform based preconditioning for a structure preserving stabilized scheme approximating the space-fractional Allen Cahn equation with logarithmic potential Ahmad, Danyal Serra-Capizzano, Stefano Sohaib, Muhammad Tablino-Possio, Cristina Numerical Analysis 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. |
| title | Spectral analysis and sine transform based preconditioning for a structure preserving stabilized scheme approximating the space-fractional Allen Cahn equation with logarithmic potential |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.24387 |