On Implicit Ordinary Differential Equations
Copyright policy )On Implicit Ordinary Differential Equations
A geometric analysis of the problem \(f(x,y,y')=0\) is given which may be of value in developing numerical methods for solution near the singular points where \(fy'=0\). In particular, the approach here shows problems of switching branches when computing numerically a solution near an envelope, as noted by \textit{L. Fox} and \textit{D. F. Mayers} [ibid. 1, 377- 401 (1981; Zbl 0471.65053)]. A simple numerical method based on the geometric approach is developed.
- University of Bath United Kingdom
- University of Toronto Canada
bifurcation, implicit equations, switching branches, Nonlinear ordinary differential equations and systems, singular points, Numerical methods for initial value problems involving ordinary differential equations
bifurcation, implicit equations, switching branches, Nonlinear ordinary differential equations and systems, singular points, Numerical methods for initial value problems involving ordinary differential equations
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