The exponential trapezoidal method for semilinear integro-differential equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917609720512512 |
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| author | Ostermann, Alexander Vaisi, Nasrin |
| author_facet | Ostermann, Alexander Vaisi, Nasrin |
| contents | The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point iteration, making its implementation straightforward. Second-order convergence in time is shown in an abstract Hilbert space framework under reasonable assumptions on the problem. Numerical experiments illustrate the proven order of convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The exponential trapezoidal method for semilinear integro-differential equations Ostermann, Alexander Vaisi, Nasrin Numerical Analysis 65R20, 65M15, 45K05 The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point iteration, making its implementation straightforward. Second-order convergence in time is shown in an abstract Hilbert space framework under reasonable assumptions on the problem. Numerical experiments illustrate the proven order of convergence. |
| title | The exponential trapezoidal method for semilinear integro-differential equations |
| topic | Numerical Analysis 65R20, 65M15, 45K05 |
| url | https://arxiv.org/abs/2403.05900 |