A Variable Stepsize, Variable Order Family of Low Complexity
Victor DeCaria, Ahmet Guzel, William Layton, Yi Li
Abstract
Variable stepsize, variable order (VSVO) methods have limited impact in timestepping methods in complex applications due to their computational complexity and the difficulty in implementing them in an existing code. We introduce a family of implicit, embedded VSVO methods that require only one BDF solve at each timestep followed by adding linear combinations of the solution at previous time levels to compute solutions of different order. In particular, we construct implicit and linearly implicit VSVO methods of orders two, three, and four with the same computational complexity as variable stepsize BDF3. The choice of changing the order of the method is simple and does not require additional nonlinear system solves.