A modified particle method for semilinear hyperbolic systems with oscillatory solutions
We introduce a modified particle method for semi-linear hyperbolic systems with highly oscillatory solutions. The main feature of this modified particle method is that we do not require different families of characteristics to meet at one point. In the modified particle method, we update the ith component of the solution along its own characteristics, and interpolate the other components of the solution from their own characteristic points to the ith characteristic point. We prove the convergence of the modified particle method essentially independent of the small scale for the variable coefficient Carleman model. The same result also applies to the non-resonant Broadwell model. Numerical evidence suggests that the modified particle method also converges essentially independent of the small scale for the original Broadwell model if a cubic spline interpolation is used.
© 2004 International Press. Received November 7, 2004; accepted for publication February 2, 2004. The research of T. Hou was supported in part by NSF under the NSF FRG grant DMS-0353838 and ITR Grant ACI-0204932.
Published - FETmaa04.pdf