Before revision:  In several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications  as required using standard SDIRK techniques .
After revision:  The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications as required using standard SDIRK techniques .