An additive semi-implicit Runge–Kutta family of schemes for nonstiff systems

An additive semi-implicit third-order Runge–Kutta family of schemes for nonstiff systems of equations is presented. These schemes involve a single implicit stage and two explicit stages and posses a linear stability domain that is larger than that of explicit Runge–Kutta schemes of the same order. The improved stability domain can be useful in some problems involving large systems of equations where a few components impose too stringent time-step limitations.