Accurate Numerical Determination of the Intersection Point of the Solution of a Differential Equation with a Given Algebraic Relation

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Abstract
In this paper, the authors present an adaptation of the simple rational extrapolation scheme (Bulirsch & Stoer, 1966) to find the point of intersection of the solution curve of an ordinary differential equation with a given curve or algebraic relationship. This point could also possibly be a point of discontinuity of the derivative. The integration algorithm is illustrated with a simple example.

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