| Summary: | 碩士 === 國立新竹教育大學 === 人資處數學教育碩士班 === 96 === This thesis mainly explores the structure of turning points, bifurcation points and solution branches of a nonlinear ordinary differential equation with boundary values.
Through the shooting method, Rung-Kutta integral formula and Newton’s interactive method, the branching points are deduced and calculated out, and then using bifurcation test theorem to determine whether bifurcation points or turning points. Furthermore, within the implicit function theorem, through Liapunov-Schmidt reduction, pseudo-arclength continuation, secant-predictor and Newton’s interactive methods, all solution branch paths passing through bifurcation points are extended out.
Lastly, the study goes further by only changing one variable while fixing the rest variables to extend out respectively the solution branch path diagrams passing through branching points. The results provide the helps in further understanding of the bifurcation phenomenon and qualitative changes of the nonlinear bifurcation subject.
|
|---|
