Numerical approximation for the blow-up solutions of a partial differential equation with conserved first integral
碩士 === 國立中正大學 === 數學系應用數學研究所 === 105 === This paper studies a finite difference approximation to the fluid equation (1), whose solutions are known to become unbounded in a finite time. We consider an explicit scheme and use the idea given in [2] for the computation of blow-up solutions. We prove tha...
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| Format: | Others |
| Language: | en_US |
| Published: |
2017
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| Online Access: | http://ndltd.ncl.edu.tw/handle/383xuy |
| Summary: | 碩士 === 國立中正大學 === 數學系應用數學研究所 === 105 === This paper studies a finite difference approximation to the fluid equation (1), whose solutions are known to become unbounded in a finite time. We consider an explicit scheme and use the idea given in [2] for the computation of blow-up solutions. We prove that our numerical solutions converge to the exact solution and that the numerical blow-up time also converges to the exact blow-up time. Several numerical examples concerning the blow-up behavior of odd p and the special case p=2 are also reported.
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