SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page A1913-A1934, January 2020.
The Strang splitting method, formally of order two, can suffer from order reduction when applied to semilinear parabolic problems with inhomogeneous boundary conditions. The recent work [L. Einkemmer and A. Ostermann, SIAM J. Sci. Comput., 37, 2015; SIAM J. Sci. Comput., 38, 2016] introduces a modification of the method to avoid the reduction of order based on the nonlinearity. In this paper we introduce a new correction constructed directly from the flow of the nonlinearity and which requires no evaluation of the source term or its derivatives. The goal is twofold. One, this new modification requires only one evaluation of the diffusion flow and one evaluation of the source term flow at each step of the algorithm and it reduces the computational effort to construct the correction. Second, numerical experiments suggest it is well suited in the case where the nonlinearity is stiff. We provide a convergence analysis of the method for a smooth nonlinearity and perform numerical experiments to illustrate the performances of the new approach.

中文翻译：

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具有非均匀边界条件的半线性抛物线问题的Strang分裂方法：基于非线性流的修正

SIAM科学计算杂志，第42卷，第3期，第A1913-A1934页，2020年1月。
当应用于边界条件不均匀的半线性抛物线问题时，形式为二阶的Strang分裂方法可能会遭受阶数减少。最近的工作[L. Einkemmer和A. Ostermann，SIAM J. Sci。计算，2015年； 37；暹罗科学 [Comput。，38，2016]引入了一种方法修改方法，可以避免基于非线性的阶数降低。在本文中，我们介绍了一种直接根据非线性流构造的新校正方法，该校正方法不需要评估源项或其导数。目标是双重的。一种是，这种新的修改仅需要对扩散流进行一次评估，而对源项流进行一次评估，就可以减少构建校正所需的计算量。第二，数值实验表明，它非常适合非线性很强的情况。我们提供了一种用于平滑非线性方法的收敛性分析，并进行了数值实验以说明新方法的性能。