More on stochastic and variational approach to the lax-friedrichs scheme

研究成果: Article査読

4 被引用数 (Scopus)

抄録

A stochastic and variational aspect of the Lax-Friedrichs scheme applied to hyperbolic scalar conservation laws and Hamilton-Jacobi equations generated by space-time dependent flux functions of the Tonelli type was clarified by Soga (2015). The results for the Lax-Friedrichs scheme are extended here to show its time-global stability, the large-time behavior, and error estimates. Also provided is a weak KAM-like theorem for discrete equations that is useful in the numerical analysis and simulation of the weak KAM theory. As one application, a finite difference approximation to effective Hamiltonians and KAM tori is rigorously treated. The proofs essentially rely on the calculus of variations in the Lax-Friedrichs scheme and on the theory of viscosity solutions of Hamilton-Jacobi equations.

本文言語English
ページ(範囲)2161-2193
ページ数33
ジャーナルMathematics of Computation
85
301
DOI
出版ステータスPublished - 2016

ASJC Scopus subject areas

  • 代数と数論
  • 計算数学
  • 応用数学

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