On Implicit Ordinary Differential Equations

In a recent paper Fox & Mayers discuss the numerical solutionof implicit ordinary differential equations of the form f(x,y(x), y'(x)) = 0. They find that numerical methods can be veryunreliable near the point where f_y' = 0. In this paper we givea theoretical analysis of the problem which enables us to explainwhen to expect numerical difficulties. We suggest a possibleline of approach for the solution of such problems, and discusssome numerical examples. Research supported by the National Science Foundation, the Officeof Naval Research, the Army Research, and the Air Force Officeof Scientific Research. Travel funding provided by the Universityof Toronto and the British Council.