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 -