TITLE:
A Particle Method for the b-Equation
AUTHORS:
Zhiqiang Xing, Yong Duan, Huiyuan Wu
KEYWORDS:
Particle Method, b-Equation, Peakon Solution, Lagrangian Representation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.11,
October
28,
2014
ABSTRACT: In this paper, we apply the particle method
to solve the numerical solution of a family of non-li-near Evolutionary Partial
Differential Equations. It is called b-equation because of its bi-Hamiltonian
structure. We introduce the particle method as an approximation of these
equations in Lagrangian representation for simulating collisions between wave
fronts. Several numerical examples will be set to illustrate the feasibility of
the particle method.