Recent results have revealed a critical way in which lower order terms affect the well-posedness of the characteristic initial value problem for the scalar wave equation. The proper choice of such terms can make the Cauchy problem for scalar waves well posed even on a background spacetime with closed lightlike curves. These results provide new guidance for developing stable characteristic evolution algorithms. In this regard, we present here the finite difference version of these recent results and implement them in a stable evolution code. We describe test results which validate the code and exhibit some of the interesting features due to the lower order terms.
Babiuc, M. C., Kreiss, H. O., & Winicour, J. (2014). Testing the well-posedness of characteristic evolution of scalar waves. Classical and Quantum Gravity,31(2), 025022.