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December 2004 A modified particle method for semilinear hyperbolic systems with oscillatory solutions
R. C. Fetecau, T. Y. Hou
Methods Appl. Anal. 11(4): 573-604 (December 2004).

Abstract

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.

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R. C. Fetecau. T. Y. Hou. "A modified particle method for semilinear hyperbolic systems with oscillatory solutions." Methods Appl. Anal. 11 (4) 573 - 604, December 2004.

Information

Published: December 2004
First available in Project Euclid: 13 April 2006

zbMATH: 1100.65076
MathSciNet: MR2195371

Subjects:
Primary: 76M28
Secondary: 65Mxx

Rights: Copyright © 2004 International Press of Boston

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Vol.11 • No. 4 • December 2004
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