High-order, large time-stepping integrators for scalar hyperbolic conservation laws

In this paper, we construct a class of temporal up -to -fourth -order integrators that preserve strong stability of conservation laws for relatively large time steps. The new methods approximate the exponential functions obtained from stabilization integrating factor Runge-Kutta schemes using recursive approximations without destroying the convergence. The time delay introduced by the stabilization parameter is then quantified and eliminated using a relaxation technique. The proposed schemes are further adopted with a monotonicity-preserving conservative scheme for the spatial discretization to solve scalar hyperbolic conservation laws. Several 1D and 2D benchmark examples are given to validate the superiority and effectiveness of the proposed schemes.