Re: plot varuation
- To: mathgroup at smc.vnet.net
- Subject: [mg9625] Re: plot varuation
- From: tburton at cts.com (Tom Burton)
- Date: Fri, 14 Nov 1997 21:40:04 -0500
- Organization: Brahea Consulting
- Sender: owner-wri-mathgroup at wolfram.com
I had recommended repeated application of FindRoot to track a root as the parameter x varied. The fact that I had blasted right through a bifurcation without comment has left me a little guilty. Just in case there is any doubt out there: Simple root-tracking algorithms like one I recommended behave badly at bifurcations. In the case I presented, the algorithm chose the upper real branch as it emerged to the right from the bifurcation. If you somehow find the other real branch and track left, the algorithm will get lost at the bifurcation and wander off. It is possible to write more sophisticated tracking algorithms, but in this case I prefer to make a few contour plots of the real and imaginary parts of f[u] - lambda^(-2(gamma-1)/(gamma+1))*g[x] versus u = (uR+I uI) at several values of x and then let my own built-in image processor do the hard work. And if you need only real solutions, then graphical solutions such as Paul Abbott's are safer and more intuitive. Tom Burton