Abstract: A Runge-Kutta discontinuous Galerkin(RKDG) method for conservation law with source term is shown.The method is implemented with Strang split or unsplit methods,and is applied to solve one-dimensional conservation law with source term as well as one and two-dimensional detonation wave problems.In order to compare with the fifth-order finite volume WENO method,a special reconstruction method is proposd to calculate integration of the source term with high-order spatial accuracy.Numerical tests in one dimension show that the RKDG method has smaller errors than WENO method for nonstiff problems and is more accurate in capturing position of discontinuity in stiff problems.Numerical simulations of detonation waves demonstrate that the RKDG method is more effcient in resolving detailed structure of detonation waves and location of detonation front.

Key words: Runge-Kutta discontinuous Galerkin method, detonation wave, reactive Euler equations, stiff source term