Report 1996-15

Contour Plots of Analytic Functions

W. Gautschi and J. Waldvogel

Abstract: This is a tutorial on generating contour lines of an analytic function $f(z)$. The emphasis is on using mathematical software (MATLAB, to a lesser extent MAPLE) for implementing the algorithms, and efficient programs together with explanations are presented. Two different approaches are suggested: (1) generating level lines as contours of, e.g., constant modulus or constant phase of the function $f(z)$, (2) setting up and numerically integrating an appropriate differential equation for the contour under consideration. Both methods are demonstrated by means of the $n$th partial sum $f(z)=e_n(z)$ of the exponential series. The line of constant modulus satisfying $|e_n(z)|=1$ has a practical significance: it delineates the region of absolute stability for an explicit Taylor integrator of order $n$.

Paper: Available as PDF (683 KB) or as hardcopy to order reports@sam.math.ethz.ch.

Publishing information: Solving Problems in Scientific Computing using Maple and MATLAB. Editors: W. Gander, J. Hrebicek. Springer Verlag, third edition, (1997), to appear