 |
Finding numerical solutions describing bubble nucleation is notoriously dicult in more than one eld space dimension. Traditional shooting methods fail because of the extreme non-linearity of eld evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of elds due to their dependence on the high dimensionality of discretized function spaces. We present a new method for nding solutions which is both very ecient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically nds solutions involving three elds in around a minute, and can nd solutions for eight elds in about an hour. We include a numerical package for Mathematica which implements the method described here.
|
|
For the newest resources, visit Wolfram Repositories and Archives »
