Strong stability preserving (SSP) Runge-Kutta methods are desirable when evolving in time problems that have discontinuities or sharp gradients and require nonlinear non-inner-product stability properties to be satisfied. Unlike the case for L2 linear stability, implicit methods do not significantly alleviate the time-step restriction when the SSP property is needed. For this reason, when handling problems with a linear component that is stiff and a nonlinear component that is not, SSP integrating factor Runge--Kutta methods may offer an attractive alternative to traditional time-stepping methods. The strong stability properties of integrating factor Runge--Kutta methods where the transformed problem is evolved with an explicit SSP Runge--Kutta method with non-decreasing abscissas was recently established. In this work, we consider the use of downwinded spatial operators to preserve the strong stability properties of integrating factor Runge--Kutta methods where the Runge--Kutta method 查看全文>>