臺灣博碩士論文加值系統

We consider the semi-linear parabolic blow-up problem u_t=u_{xx}+f(u)
(0<x<1, t>0) with certain choices of f and their finite difference analogues whose solutions also blow up in finite time. In this paper, we are going to classify the exact numerical blow-up sets. It is interesting that despite of the convergence of the numerical solutions and the numerical blow-up time, the numerical blow-up sets do not always coincide with that of the PDE. However, the blow-up shapes seem to be realized by our difference schemes.

1 Introduction 1
2 Explicit scheme 4
3 f(u)=u^2[log(1+u)]^\beta 9
4 Implicit + Explicit scheme by \theta 14
5 Numerical Experiments 19

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