High order operator splitting methods based on an integral deferred correction framework
Document Type
Article
Publication Date
8-1-2015
Abstract
© 2015 Elsevier Inc. 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.
Publication Title
Journal of Computational Physics
Recommended Citation
Christlieb, A.,
Liu, Y.,
&
Xu, Z.
(2015).
High order operator splitting methods based on an integral deferred correction framework.
Journal of Computational Physics,
294, 224-242.
http://doi.org/10.1016/j.jcp.2015.03.032
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6667