### 抜粋

We provide an accurate verification method for solutions of heat equations with a superlinear nonlinearity. The verification method numerically proves the existence and local uniqueness of the exact solution in a neighborhood of a numerically computed approximate solution. Our method is based on a fixed-point formulation using the evolution operator, an iterative numerical verification scheme to extend a time interval in which the validity of the solution can be verified, and rearranged error estimates for avoiding the propagation of an overestimate. As a result, compared with the previous verification method using the analytic semigroup, our method can enclose the solution for a longer time. Some numerical examples are presented to illustrate the efficiency of our verification method.

元の言語 | English |
---|---|

ページ（範囲） | 74-99 |

ページ数 | 26 |

ジャーナル | Reliable Computing |

巻 | 25 |

出版物ステータス | Published - 2017 |

### ASJC Scopus subject areas

- Software
- Computational Mathematics
- Applied Mathematics

## フィンガープリント Accurate method of verified computing for solutions of semilinear heat equations' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*Reliable Computing*,

*25*, 74-99.