Methods and Applications of Analysis

A modified particle method for semilinear hyperbolic systems with oscillatory solutions

R. C. Fetecau and T. Y. Hou

Full-text: Open access

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.

Article information

Source
Methods Appl. Anal. Volume 11, Number 4 (2004), 573-604.

Dates
First available in Project Euclid: 13 April 2006

Permanent link to this document
http://projecteuclid.org/euclid.maa/1144939948

Mathematical Reviews number (MathSciNet)
MR2195371

Zentralblatt MATH identifier
1100.65076

Subjects
Primary: 76M28: Particle methods and lattice-gas methods
Secondary: 65Mxx: Partial differential equations, initial value and time-dependent initial- boundary value problems

Citation

Fetecau, R. C.; Hou, T. Y. A modified particle method for semilinear hyperbolic systems with oscillatory solutions. Methods and Applications of Analysis 11 (2004), no. 4, 573--604. http://projecteuclid.org/euclid.maa/1144939948.


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