常微分方程式系の解の爆発時刻および爆発レートの推定法 : 偏微分方程式の爆発問題への応用

概要

論文の詳細を見る
A numerical method is proposed for estimating the blow-up time and blow-up rate of the solution of the system of ordinary differential equations (ODEs), whose solution has a pole at a finite time, that is, the blow-up time. The main idea is to transform the ODE system into a tractable form by Moriguti's technique, and to generate a linearly convergent sequence to the blow-up time. The sequence is accelerated by the Aitken Δ^2 method. The present method is applied to the problem of finding the blow-up time of the solution of partial differential equations (PDEs), by discretizing the PDEs in space. Numerical experiments on the two PDEs, the semilinear reaction-diffusion equation and the heat equation with a nonlinear boundary condition, show the validity of the present method.
日本応用数理学会の論文
2004-03-25