标题： 扩散-反应问题的初始边界修正分裂方法 显示英文标题

标题： An initial-boundary corrected splitting method for diffusion-reaction problems

摘要： 奇异分裂是一种广泛用于求解扩散-反应问题的二阶方法。 然而，其收敛阶通常对于狄利克雷边界条件会降低到阶$1$，对于诺伊曼和罗宾边界条件会降低到阶$1.5$，导致精度降低和效率减少。 在本文中，我们提出了一种新的分裂方法，称为初始-边界校正分裂，该方法避免了阶数降低，同时提高了更广泛应用范围内的计算效率。 与文献中提出的校正方法不同，它不需要计算依赖于边界条件和边界数据的校正项。 通过严格的分析收敛性分析和数值实验，我们展示了所提出方法的改进精度和性能。 显示英文摘要

摘要： Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order $1$ for Dirichlet boundary conditions and to order $1.5$ for Neumann and Robin boundary conditions, leading to lower accuracy and reduced efficiency. In this paper, we propose a new splitting approach, called an initial-boundary corrected splitting, which avoids order reduction while improving computational efficiency for a wider range of applications. In contrast to the corrections proposed in the literature, it does not require the computation of correction terms that depend on the boundary conditions and boundary data. Through rigorous analytical convergence analysis and numerical experiments, we demonstrate the improved accuracy and performance of the proposed method.