Accurate method of verified computing for solutions of semilinear heat equations

Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, Shin'ichi Oishi

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)74-99
ページ数26
ジャーナルReliable Computing
25
出版ステータスPublished - 2017

ASJC Scopus subject areas

  • ソフトウェア
  • 計算数学
  • 応用数学

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