On a Finite Difference Scheme for Blow Up Solutions of a Semilinear Parabolic System
碩士 === 國立中正大學 === 數學系應用數學研究所 === 106 === 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 equati...
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2018
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ndltd-TW-105CCU005070122019-05-16T00:30:08Z http://ndltd.ncl.edu.tw/handle/n8ej6f On a Finite Difference Scheme for Blow Up Solutions of a Semilinear Parabolic System 用有限差分計算一個半線性拋物方程組爆炸解的近似值 LU, YING-JUNG 呂映蓉 碩士 國立中正大學 數學系應用數學研究所 106 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. Cho, Chien-Hong 卓建宏 2018 學位論文 ; thesis 19 en_US |
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NDLTD |
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碩士 === 國立中正大學 === 數學系應用數學研究所 === 106 === 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.
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| author2 |
Cho, Chien-Hong |
| author_facet |
Cho, Chien-Hong LU, YING-JUNG 呂映蓉 |
| author |
LU, YING-JUNG 呂映蓉 |
| spellingShingle |
LU, YING-JUNG 呂映蓉 On a Finite Difference Scheme for Blow Up Solutions of a Semilinear Parabolic System |
| author_sort |
LU, YING-JUNG |
| title |
On a Finite Difference Scheme for Blow Up Solutions of a Semilinear Parabolic System |
| title_short |
On a Finite Difference Scheme for Blow Up Solutions of a Semilinear Parabolic System |
| title_full |
On a Finite Difference Scheme for Blow Up Solutions of a Semilinear Parabolic System |
| title_fullStr |
On a Finite Difference Scheme for Blow Up Solutions of a Semilinear Parabolic System |
| title_full_unstemmed |
On a Finite Difference Scheme for Blow Up Solutions of a Semilinear Parabolic System |
| title_sort |
on a finite difference scheme for blow up solutions of a semilinear parabolic system |
| publishDate |
2018 |
| url |
http://ndltd.ncl.edu.tw/handle/n8ej6f |
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