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研究生:呂映蓉
研究生(外文):LU, YING-JUNG
論文名稱:用有限差分計算一個半線性拋物方程組爆炸解的近似值
論文名稱(外文):On a Finite Difference Scheme for Blow Up Solutions of a Semilinear Parabolic System
指導教授:卓建宏卓建宏引用關係
指導教授(外文):Cho, Chien-Hong
口試委員:林敏雄黃博峙
口試日期:2018-06-14
學位類別:碩士
校院名稱:國立中正大學
系所名稱:數學系應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:英文
論文頁數:19
外文關鍵詞:finite differencenumerical blow-up timesemi-linear heat equation
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The finite-time blow-up phenomenon for the semilinear heat equation was widely considered since 1960's both mathematically and numerically. In this paper, we would like to consider the computation of blow-up solutions for a coupled semilinear heat equations. To this end, we study the numerical solutions for an ODE system as a first step. We propose a scheme for the computation of the numerical blow-up time and prove the convergence for the numerical solution and the numerical blow-up time. Then we apply the idea to a semilinear parabolic system whose solution may blow up in a finite time. Several numerical examples are reported and discussed.
Abstract i
Contents ii
List of Figures iii
1 Introduction 1
2 A nonlinear ODE system 3
3 A finite difference scheme for (4) 10
4 Conclusion 17
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