Variable step-size fractional step Runge–Kutta methods for time-dependent partial differential equations

Fractional step Runge–Kutta methods are a class of additive Runge–Kutta schemes that provide efficient time discretizations for evolutionary partial differential equations. This efficiency is due to appropriate decompositions of the elliptic operator involving the spatial derivatives. In this work, we tackle the design and analysis of embedded pairs of fractional step Runge–Kutta methods. Such methods suitably estimate the local error at each time step, thus providing efficient variable step-size time integrations. Finally, some numerical experiments illustrate the behaviour of the proposed algorithms.