TY - JOUR
T1 - A self-adaptive moving mesh method for the Camassa-Holm equation
AU - Feng, Bao Feng
AU - Maruno, Ken Ichi
AU - Ohta, Yasuhiro
N1 - Funding Information:
The work of B.F. was partially supported by the US Army Research Office under Contract No. W911NF-05-1-0029. The work of Y.O. was partly supported by JSPS Grant-in-Aid for Scientific Research ( B-19340031 , S-19104002 ). Y.O. and K.M. are grateful for the hospitality of the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge where this article was completed during the programme Discrete Integrable Systems (DIS). The authors are grateful to the anonymous referee for valuable comments.
PY - 2010/11/1
Y1 - 2010/11/1
N2 - A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is evolved, the solution is determined by solving a tridiagonal linear system. Due to these two superior features of the method, several test problems give very satisfactory results even if by using a small number of grid points.
AB - A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is evolved, the solution is determined by solving a tridiagonal linear system. Due to these two superior features of the method, several test problems give very satisfactory results even if by using a small number of grid points.
KW - Integrable semi-discretization
KW - Peakon and cupson solutions
KW - Self-adaptive moving mesh method
KW - The Camassa-Holm equation
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U2 - 10.1016/j.cam.2010.05.044
DO - 10.1016/j.cam.2010.05.044
M3 - Article
AN - SCOPUS:77955419330
SN - 0377-0427
VL - 235
SP - 229
EP - 243
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1
ER -