标题： 克服在非周期边界条件下应用于半线性抛物问题的分裂方法中的阶次障碍二 显示英文标题

标题： Overcoming the order barrier two in splitting methods when applied to semilinear parabolic problems with non-periodic boundary conditions

摘要： 一般来说，当将高阶分裂方法应用于具有非周期边界条件的偏微分方程的时间积分时，会经历阶数降低的现象。 在过去十年中，引入了几种修改方法，以防止二阶Strang分裂方法出现这种现象。 在本文中，受这些最近的校正技术启发，我们为一类半线性抛物问题引入了一种三阶分裂方法，在非周期边界条件的背景下避免了阶数降低。 我们在一个简化的线性设置中给出了该方法三阶收敛的证明，并通过数值实验验证了这一结果。 此外，我们数值地展示了高阶收敛性在分裂方法的四阶变体以及非线性源项的情况下仍然存在。 显示英文摘要

摘要： 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.