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Integral deferred correction (IDC) methods have been shown to be an efficientway to achieve arbitrary high order accuracy and possess good stabilityproperties. In this paper, we construct high order operator splitting schemesusing the IDC procedure to solve initial value problems (IVPs). We presentanalysis to show that the IDC methods can correct for both the splitting andnumerical 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 correctionequation. We further apply this framework to solve partial differentialequations (PDEs). Numerical examples in two dimensions of linear and nonlinearinitial-boundary value problems are presented to demonstrate the performance ofthe proposed IDC approach.

High order operator splitting methods based on an integral deferred correction framework