| Summary: | 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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