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A Particle Method And Numerical Study Of A Quasilinear Partial Differential Equation, R. Camassa, P. H. Chiu, Long Lee, T.W.H. Sheu
A Particle Method And Numerical Study Of A Quasilinear Partial Differential Equation, R. Camassa, P. H. Chiu, Long Lee, T.W.H. Sheu
Long Lee
We present a particle method for studying a quasilinear partial differential equation (PDE) in a class proposed for the regularization of the Hopf (inviscid Burger) equation via nonlinear dispersion-like terms. These are obtained in an advection equation by coupling the advecting field to the advected one through a Helmholtz operator. Solutions of this PDE are "regularized" in the sense that the additional terms generated by the coupling prevent solution multivaluedness from occurring. We propose a particle algorithm to solve the quasilinear PDE. "Particles" in this algorithm travel along characteristic curves of the equation, and their positions and momenta determine the …