Local convergence analysis of a linearized Alikhanov scheme for the time fractional sine-Gordon equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912855013457920 |
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| author | Hou, Chang Chen, Hu |
| author_facet | Hou, Chang Chen, Hu |
| contents | This paper investigates the time fractional sine-Gordon equation whose solution exhibits a weak singularity of type t^α. By means of the Alikhanov formula we derive a fully discrete, linearized scheme. Using the more general regularity assumption, we derive a sharp truncation-error bound for the fractional derivative. Furthermore, we prove a key inequality and a less restrictive stability result that is valid on general graded temporal meshes. Consequently, the temporal local convergence order is shown to be min{2, r} in H^1-seminorm, where r is the degree of grading; numerical experiments confirm that the optimal rate is already attained as soon as r = 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20566 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local convergence analysis of a linearized Alikhanov scheme for the time fractional sine-Gordon equation Hou, Chang Chen, Hu Numerical Analysis This paper investigates the time fractional sine-Gordon equation whose solution exhibits a weak singularity of type t^α. By means of the Alikhanov formula we derive a fully discrete, linearized scheme. Using the more general regularity assumption, we derive a sharp truncation-error bound for the fractional derivative. Furthermore, we prove a key inequality and a less restrictive stability result that is valid on general graded temporal meshes. Consequently, the temporal local convergence order is shown to be min{2, r} in H^1-seminorm, where r is the degree of grading; numerical experiments confirm that the optimal rate is already attained as soon as r = 2. |
| title | Local convergence analysis of a linearized Alikhanov scheme for the time fractional sine-Gordon equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.20566 |