On the Numerical Blow-up Set for the Semi-linear Heat Equation
碩士 === 國立中正大學 === 應用數學研究所 === 99 === 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 bl...
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| Format: | Others |
| Language: | en_US |
| Published: |
2011
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| Online Access: | http://ndltd.ncl.edu.tw/handle/86620925437710064503 |
| Summary: | 碩士 === 國立中正大學 === 應用數學研究所 === 99 === 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.
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