A Computer Graphics Method for Solving Transcendental Equations

Abstract : Finding the roots of an equation F(x)=0 when F(x) involves transcendental functions and x is complex usually involves some kind of search method. The efficiency of a search method depends to a certain extent on knowledge of the roots--where they are likely to occur in the x plane, and how many there are. If a root is known to lie in a given region in the x plane, then a search routine can quickly find the root to the desired accuracy. But if no information about the location of the roots is available, a search over a wide area must be conducted, and this can be time consuming and expensive. Consequently, a method for locating the general area of the roots and determining the pattern of the roots is very valuable. The report describes a simple method for graphically displaying the pattern of roots in the complex plane.