The n-dimensional Laplace equation is of the form:
The determining systems for this equation are the simplest that we have posted Lie symmetry determining systems for.
The determining system consists of the dependent variables and X01, X02,..., Xn which depend on the independent variables and x01, x02,..., xn.
The systems for n = 3..16 can be downloaded here (the files in the archive are named laplace_n). It should be emphasized that these are test systems only, as they are homogeneous constant coefficient PDE in the infinitesimals, and are relatively easy to bring to simplified form (as can be seen by the run-times below).
|Dimension||Equations||Length||Time (sec)||Mem (MB)|