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- W4381570794 abstract "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." @default.
- W4381570794 created "2023-06-22" @default.
- W4381570794 creator A5092230161 @default.
- W4381570794 date "2023-06-19" @default.
- W4381570794 modified "2023-09-23" @default.
- W4381570794 title "Overcoming the order barrier two in splitting methods when applied to semilinear parabolic problems with non-periodic boundary conditions" @default.
- W4381570794 doi "https://doi.org/10.48550/arxiv.2306.10966" @default.
- W4381570794 hasPublicationYear "2023" @default.
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