Determination of the Intersection Points of Two
Plane Curves by Means of Differential Equations

A new method is proposed to calculate the intersection
points of two plane curves.  The theory 
of singular points off a system of two differential equations
is used in developing the method. The intersection 
point to be determined is identified with such a singular
point and appropriate modifications are applied 
to the system to ensure that the singular point be stable,
i.e. all integrals which start in the neighborhood 
of the singular point will always approach this point
if the integral parameter tends to infinity.  In 
addition a method is described for systematically searching
for all intersection points in a prescribed 
rectangular area.

CACM July, 1968

Kuiken, H. K.

plane curves, intersection points, intersections
plane curves, integration, differential equations, 
matrix iteration, singular points, nonlinear differential
equations, eigenvalues, complex roots, roots, 
stationary points, Runge Kutta, stable singularity, unstable singularity

2.0 3.10 3.20 3.50 5.10

CA680708 JB February 22, 1978  11:51 AM

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