论文标题
基于自适应LOOCV的内核方法，用于求解时间依赖性BVP
Adaptive LOOCV-based kernel methods for solving time-dependent BVPs
论文作者
论文摘要
在本文中，我们提出了一种自适应方案，以解决时间依赖的边界价值问题（BVP）。为了通过数值解决这些问题，我们考虑了基于内核的线方法，该方法使我们能够分别分别处理每个空间和时间导数。该自适应算法基于保留的交叉验证（LOOCV）技术，该技术被用作误差指标。通过此方案，我们可以首先检测到误差估计太大的域区域 - 通常是由于解决方案的急剧变化或快速变化，然后相应地通过应用两点完善策略来增强数值解决方案。数值实验显示了我们自适应改进方法的功效和性能。
In this paper we propose an adaptive scheme for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel-based method of lines that allows us to split the spatial and time derivatives, dealing with each separately. This adaptive algorithm is based on a leave-one-out cross validation (LOOCV) technique, which is employed as an error indicator. By this scheme, we can first detect the domain areas where the error is estimated to be too large -- generally due to steep variations or quick changes in the solution -- and then accordingly enhance the numerical solution by applying a two-point refinement strategy. Numerical experiments show the efficacy and performance of our adaptive refinement method.
