Here, SSPRK3 refers to third order strong stability preserving Runge-Kutta and RK3 refres to regular third order Runge-Kutta method. The meaning of the method is obvious from the name. However there is a restriction while one is choosing the time step. It is mentioned in "Strong stability preserving high-order time discretization methods" by Gottlieb, Shu , and Tadmor. Since my problem is nonliner systems of hyperbolic PDEs (partial differential equations), related part about my problem is in the section 4.1. The question is that what is the interaction between CFL condition and strong stability preserving coefficient ?