Deferred Correction Methods and Time Compact Methods for the Time Discretization of Initial Boundary Value Problems

We present two different methods for achieving high order accurate, unconditionally stable time stepping schemes for the treatment of partial differential equations. Unconditionally stable schemes are necessary for so called stiff problems where stability restrictions lead to an extremely small upper bound for the admissible time step. When considering higher order methods in time, the stability domain is often considerably decreased. The methods we consider are deferred correction methods and time compact methods. They lead to unconditionally stable schemes for arbitrarily high order accuracy.