Open access
Date
1996-10Type
- Report
ETH Bibliography
yes
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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 $n$. Show more
Permanent link
https://doi.org/10.3929/ethz-a-004284538Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichOrganisational unit
02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics
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ETH Bibliography
yes
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