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Unformatted text preview: bsolute-stability region is determined as
; 1 + z = ei
which can easily be recognized as the familiar unit circle centered at z = ;1 + 0i. For
real values of z the intervals of absolute stability for methods with p = s 4 are shown
in Table 3.2.3. Absolute stability regions for complex values of z are illustrated for the
same methods in Figure 3.2.1. Methods are stable within the closed regions shown. The
regions of absolute stability grow with increasing p. When p = 3 4, they also extend
slightly into the right half of the complex z-plane. Problems 1. Instead of solving the IVP (3.1.1), many software systems treat an autonomous
ODE y = f (y). Non-autonomous ODEs can be written as autonomous systems
0 16 Order, p Interval of
Table 3.2.3: Interval of absolute stability for p-stage explicit Runge-Kutta methods of
order p = 1 2 3 4. 3 2 Im(z) 1 0 −1 −2 −3
−5 −4 −3 −2
Re(z) −1 0 Figure 3.2.1: Region of absolute stability for p-stage explicit R...
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This document was uploaded on 03/16/2014 for the course CSCI 6820 at Rensselaer Polytechnic Institute.
- Spring '14