WENO/RK method for modelling elastic waves

High accuracy WENO-Runge-Kutta numerical method is developed for solving linear elasticity equations written in the form of hyperbolic system of conservation laws. Methods up to the 5th order in space and 4th order in time have been considered. Numerical results obtained for some test problems by the developed methods are much more accurate in comparison with those obtained by the commonly used Virieux scheme of the second order in space and time. Implementation of the PML strategy into the developed methods is also considered.