### Abstract

In the simulations of Burridge-Knopoff (BK) model of earthquakes, the friction force laws are important to produce earthquake-like stick-slip behaviors. Some friction force laws are set-valued and the BK model with them can produce consistent results with observed data of earthquakes in some aspects. However, it is cumbersome to simulate the BK model with set-valued laws by conventional explicit integration methods. In the presence of set-valued laws, the explicit integration methods can easily lead to the numerical chattering, violated constraints on the velocity of force laws, and the difficulty of identifying the states of blocks of the BK model. This paper employs an implicit Euler integration method to simulate the BK model with symmetric and asymmetric set-valued laws. This method removes the numerical chattering in the BK model, even in the cases of large time step sizes. It can easily detect the stuck or slipping state of a block element. Comparing to previous results integrated by explicit integration methods in the literature, the results integrated by this implicit method show smoother curves and lower irregularities in the magnitude distribution of events.

Original language | English |
---|---|

Pages (from-to) | 1039-1057 |

Number of pages | 19 |

Journal | Advances in Computational Mathematics |

Volume | 41 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Advances in Computational Mathematics*,

*41*(6), 1039-1057. https://doi.org/10.1007/s10444-014-9398-4

**Implicit Euler simulation of one-dimensional Burridge-Knopoff model of earthquakes with set-valued friction laws.** / Xiong, Xiaogang; Kikuuwe, Ryo; Yamamoto, Motoji.

Research output: Contribution to journal › Article

*Advances in Computational Mathematics*, vol. 41, no. 6, pp. 1039-1057. https://doi.org/10.1007/s10444-014-9398-4

}

TY - JOUR

T1 - Implicit Euler simulation of one-dimensional Burridge-Knopoff model of earthquakes with set-valued friction laws

AU - Xiong, Xiaogang

AU - Kikuuwe, Ryo

AU - Yamamoto, Motoji

PY - 2015/12/1

Y1 - 2015/12/1

N2 - In the simulations of Burridge-Knopoff (BK) model of earthquakes, the friction force laws are important to produce earthquake-like stick-slip behaviors. Some friction force laws are set-valued and the BK model with them can produce consistent results with observed data of earthquakes in some aspects. However, it is cumbersome to simulate the BK model with set-valued laws by conventional explicit integration methods. In the presence of set-valued laws, the explicit integration methods can easily lead to the numerical chattering, violated constraints on the velocity of force laws, and the difficulty of identifying the states of blocks of the BK model. This paper employs an implicit Euler integration method to simulate the BK model with symmetric and asymmetric set-valued laws. This method removes the numerical chattering in the BK model, even in the cases of large time step sizes. It can easily detect the stuck or slipping state of a block element. Comparing to previous results integrated by explicit integration methods in the literature, the results integrated by this implicit method show smoother curves and lower irregularities in the magnitude distribution of events.

AB - In the simulations of Burridge-Knopoff (BK) model of earthquakes, the friction force laws are important to produce earthquake-like stick-slip behaviors. Some friction force laws are set-valued and the BK model with them can produce consistent results with observed data of earthquakes in some aspects. However, it is cumbersome to simulate the BK model with set-valued laws by conventional explicit integration methods. In the presence of set-valued laws, the explicit integration methods can easily lead to the numerical chattering, violated constraints on the velocity of force laws, and the difficulty of identifying the states of blocks of the BK model. This paper employs an implicit Euler integration method to simulate the BK model with symmetric and asymmetric set-valued laws. This method removes the numerical chattering in the BK model, even in the cases of large time step sizes. It can easily detect the stuck or slipping state of a block element. Comparing to previous results integrated by explicit integration methods in the literature, the results integrated by this implicit method show smoother curves and lower irregularities in the magnitude distribution of events.

UR - http://www.scopus.com/inward/record.url?scp=84949101670&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949101670&partnerID=8YFLogxK

U2 - 10.1007/s10444-014-9398-4

DO - 10.1007/s10444-014-9398-4

M3 - Article

AN - SCOPUS:84949101670

VL - 41

SP - 1039

EP - 1057

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

SN - 1019-7168

IS - 6

ER -