APPLYING HIGHER-ORDER DIRK TIME STEPS TO THE MODIFIED PICARD METHOD

The ''modified Picard'' iteration method, which offers global mass conservation, can also be described as a form of Newton's iteration with lagged nonlinear coefficients. It converges to a time step with first-order discretization error. This paper applies second- and third-order diagonally implicit Runge gutta (DIRK) time steps to the modified Picard method in one example. It demonstrates improvements over the first-order time step in rms error and error-times-effort model quality by factors ranging from two to over two orders of magnitude, showing that the ''modified Picard'' and DIRK methods are compatible.