Jacobian-Free Explicit Multiderivative Runge–Kutta Methods for Hyperbolic Conservation Laws

Based on the recent development of Jacobian-free Lax–Wendroff (LW) approaches for solving hyperbolic conservation laws (Zorio et al. in J Sci Comput 71:246–273, 2017, Carrillo and Parés 80:1832–1866, 2019), a novel collection explicit multistage multiderivative solvers is presented this work. In contrast to Taylor time-integration methods, Runge–Kutta (MDRK) techniques achieve higher-order consistency not only through excessive addition higher temporal derivatives, but also Runge–Kutta-type stages. This adds more flexibility time integration such way that stable efficient schemes could be identified. The method permits practical application MDRK schemes. their original form, they are difficult utilize as flux derivatives have computed analytically. Here we overcome by adopting approximation those derivatives. paper, analyze with respect order stability. We show linear CFL number varies significantly used. Results verified numerically several representative testcases.