The bifurcation and continuation of solution paths of a nonlinear two-point boundary valued ordinary differential equation
碩士 === 國立新竹教育大學 === 人資處數學教育碩士班 === 94 === Abstract In this thesis, we use the bifurcation at a simple eigenvalue to compute the possible bifurcation points of two nonlinear two-point boundary valued ordinary differential equations, and then use the implicit function theorem, the direction of solutio...
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2005
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ndltd-TW-094NHCT54800072015-10-13T10:34:46Z http://ndltd.ncl.edu.tw/handle/41768166808294493133 The bifurcation and continuation of solution paths of a nonlinear two-point boundary valued ordinary differential equation 非線性兩點邊界值常微分方程解路徑之分歧與延拓 梁寶丹 碩士 國立新竹教育大學 人資處數學教育碩士班 94 Abstract In this thesis, we use the bifurcation at a simple eigenvalue to compute the possible bifurcation points of two nonlinear two-point boundary valued ordinary differential equations, and then use the implicit function theorem, the direction of solution branches, secant predictor method, Newton’s iterative method, and pseudo–arclength continuation method to figure out the solution paths of the buckling of an elastic rod and the other model. We get solution branches of the models, and find a lot of bifurcation points and turning points which help us to understand the qualitative analysis in the nonlinear bifurcation problems 簡國清 2005 學位論文 ; thesis 68 zh-TW |
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碩士 === 國立新竹教育大學 === 人資處數學教育碩士班 === 94 === Abstract
In this thesis, we use the bifurcation at a simple eigenvalue to compute the possible bifurcation points of two nonlinear two-point boundary valued ordinary differential equations, and then use the implicit function theorem, the direction of solution branches, secant predictor method, Newton’s iterative method, and pseudo–arclength continuation method to figure out the solution paths of the buckling of an elastic rod and the other model. We get solution branches of the models, and find a lot of bifurcation points and turning points which help us to understand the qualitative analysis in the nonlinear bifurcation problems
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| author2 |
簡國清 |
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簡國清 梁寶丹 |
| author |
梁寶丹 |
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梁寶丹 The bifurcation and continuation of solution paths of a nonlinear two-point boundary valued ordinary differential equation |
| author_sort |
梁寶丹 |
| title |
The bifurcation and continuation of solution paths of a nonlinear two-point boundary valued ordinary differential equation |
| title_short |
The bifurcation and continuation of solution paths of a nonlinear two-point boundary valued ordinary differential equation |
| title_full |
The bifurcation and continuation of solution paths of a nonlinear two-point boundary valued ordinary differential equation |
| title_fullStr |
The bifurcation and continuation of solution paths of a nonlinear two-point boundary valued ordinary differential equation |
| title_full_unstemmed |
The bifurcation and continuation of solution paths of a nonlinear two-point boundary valued ordinary differential equation |
| title_sort |
bifurcation and continuation of solution paths of a nonlinear two-point boundary valued ordinary differential equation |
| publishDate |
2005 |
| url |
http://ndltd.ncl.edu.tw/handle/41768166808294493133 |
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