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Manuscript Title: NULLIJN: a program to calculate zero curves of a function of two variables of which one may be complex.
Authors: P.C. de Jagher
Program title: NULLIJN
Catalogue identifier: ACYL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 15(1978)351
Programming language: Fortran, Compass.
Computer: CDC CYBER 73/173.
Operating system: NOS/BE 1.1.
Program overlaid: yes
RAM: 51K words
Word size: 60
Peripherals: graph plotter, disc.
Keywords: General purpose, Implicitly defined Function, Zero curve, Plasma dispersion, Potential problem.
Classification: 4.7.

Nature of problem:
When an algorithm for a function f of two variables, for instance a dispersion function f(w,k) or a potential V(r,z) is known, the program calculates and plots the zero curves, thus giving a graphical representation of an implicitly defined function. One of the variables may be complex.

Solution method:
A quadratic extrapolation, followed by a regula falsi algorithm to find a zero is used to calculate a succession of zero-points along a curve. The starting point of a curve is found by detecting a change of sign of the function on the edge of the area G that is examined.

Curves that lie entirely inside G are not found. Starting points of curves where the imaginary part of the complex variable is large might be missed.

Running time:
The running time depends on the kind of function that is investigated. The algorithm for the evaluation of the function is usually executed 2000 - 30000 times.