Modifications to the Lax-Wendroff scheme for hyperbolic systems with source terms

For wave phenomena in one spatial dimension, governed by hyperbolic partial di erential equations with source terms, the standard Lax{Wendro scheme leads to oscillations at discontinuous wavefronts even if the Courant{Friedrich{Lewy (CFL) number is set equal to unity. We modify the Lax{Wendro scheme for hyperbolic systems with source terms based on characteristic analysis to preserve the wave pro le correctly when the CFL number is set equal to 1. The new scheme can be used as easily as the original Lax{Wendro scheme since the calculation of the characteristics is not introduced in the new scheme. Thus, additional computations of characteristics are not necessary. We also extend our method for higher spatial dimensions and illustrate our approach by numerical examples. Copyright