MAKE A MEME
View Large Image
| View Original: | Stability region for BDF1.svg (576x432) | |||
| Download: | Original | Medium | Small | Thumb |
| Courtesy of: | commons.wikimedia.org | More Like This | ||
| Keywords: Stability region for BDF1.svg en Region of absolute stability for the backward Euler BDF1 method See below for Python source Compare with page 350 of Süli Endre; Mayers David 2003 An Introduction to Numerical Analysis Cambridge University Press ISBN 0521007941 2012-03-20 own Jitse Niesen cc-zero Source code The image has produced by the following code which was inspired by the source code for File Stability region for Euler method svg <source lang python > import numpy from matplotlib import pyplot BFDcoeffs 1 'alpha' 1 -1 'beta' 1 2 'alpha' 3 -4 1 'beta' 2 3 'alpha' 11 -18 9 -2 'beta' 6 4 'alpha' 25 -48 36 -16 3 'beta' 12 5 'alpha' 137 -300 300 -200 75 -12 'beta' 60 6 'alpha' 147 -360 450 -400 225 -72 'beta' 60 plotWindow 1 'realPart' -2 3 'imagPart' -2 2 2 'realPart' -2 5 'imagPart' -3 3 3 'realPart' -4 8 'imagPart' -5 5 4 'realPart' -4 14 'imagPart' -8 8 5 'realPart' -10 25 'imagPart' -15 15 6 'realPart' -20 40 'imagPart' -30 30 Returns > 1 if argument is not in region of absolute stability def stabilityFunction hTimesLambda s stabPolyCoeffs list BFDcoeffss'alpha' stabPolyCoeffs0 - hTimesLambda BFDcoeffss'beta' return max abs numpy roots stabPolyCoeffs Main program for s in range 1 7 x numpy linspace plotWindows'realPart' num 400 y numpy linspace plotWindows'imagPart' num 400 X Y numpy meshgrid x y Z numpy zeros X shape for m in range X shape0 for n in range X shape1 Zm n stabilityFunction Xm n + 1j Ym n s pyplot contour X Y Z 1 colors 'k' pyplot contourf X Y Z 0 1 colors 1 0 5 0 8 pyplot plot plotWindows'realPart' 0 0 'k--' pyplot plot 0 0 plotWindows'imagPart' 'k--' pyplot gca tick_params labelsize 20 pyplot savefig 'Stability_region_for_BDF d svg' s pyplot clf </source> Uploaded with UploadWizard Stability regions Created with Matplotlib Images with Python source code | ||||
