Overcoming the order barrier two in splitting methods when applied to semilinear parabolic problems with non-periodic boundary conditions
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910106079199232 |
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| author | Häberli, Ramona |
| author_facet | Häberli, Ramona |
| contents | In general, high order splitting methods suffer from an order reduction phenomena when applied to the time integration of partial differential equations with non-periodic boundary conditions. In the last decade, there were introduced several modifications to prevent the second order Strang splitting method from such a phenomena. In this article, inspired by these recent corrector techniques, we introduce a splitting method of order three for a class of semilinear parabolic problems that avoids order reduction in the context of non-periodic boundary conditions. We give a proof for the third order convergence of the method in a simplified linear setting and confirm the result by numerical experiments. Moreover, we show numerically that the high order convergence persists for an order four variant of a splitting method, and also for a nonlinear source term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10966 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Overcoming the order barrier two in splitting methods when applied to semilinear parabolic problems with non-periodic boundary conditions Häberli, Ramona Numerical Analysis 65M12, 65L04 In general, high order splitting methods suffer from an order reduction phenomena when applied to the time integration of partial differential equations with non-periodic boundary conditions. In the last decade, there were introduced several modifications to prevent the second order Strang splitting method from such a phenomena. In this article, inspired by these recent corrector techniques, we introduce a splitting method of order three for a class of semilinear parabolic problems that avoids order reduction in the context of non-periodic boundary conditions. We give a proof for the third order convergence of the method in a simplified linear setting and confirm the result by numerical experiments. Moreover, we show numerically that the high order convergence persists for an order four variant of a splitting method, and also for a nonlinear source term. |
| title | Overcoming the order barrier two in splitting methods when applied to semilinear parabolic problems with non-periodic boundary conditions |
| topic | Numerical Analysis 65M12, 65L04 |
| url | https://arxiv.org/abs/2306.10966 |