理学院数理讲坛（2015年第五十三讲）
报告人： Yuan Liu（Assistant Professor, Department of Mathematics and Statistics, Mississippi State University）
报告时间：2015年12月28日上午10：00
报告地点：阳明学院303报告厅
报告题目：High order operator splitting methods based on an integral deferred correction framework
报告摘要：
Integral deferred correction (IDC) methods have been shown to be an efficient
way to achieve arbitrary high order accuracy and possess good stability properties.
In this paper, we construct high order operator splitting schemes using the IDC
procedure to solve initial value problems (IVPs). We present analysis to show that
the IDC methods can correct for both the splitting and numerical errors, lifting the
order of accuracy by r with each correction, where r is the order of accuracy of the
method used to solve the correction equation. We further apply this framework to
solve partial differential equations (PDEs). Numerical examples in two dimensions
of linear and nonlinear initial-boundary value problems are presented to demonstrate
the performance of the proposed IDC approach.
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