Error Estimates for Deferred Correction Methods in Time

In this paper, we consider the deferred correction principle for high order accurate time discretization of partial differential equations (PDEs) and ordinary differential equations (ODEs). Deferred correction is based on a lower order method, here we use second order accurate A-stable methods. Solutions of higher order accuracy are computed successively. The computational complexity for calculating higher order solutions is comparable to the complexity of the lower order method. There is no stability restraint on the size of the time-step. Error estimates are derived and the application of the schemes to initial boundary value problems is discussed in detail. The theoretical results are supported by a series of numerical experiments.