A noniterative transformation method applied to two-point boundary-value problems (Q919763)

The numerical integration of (*) \(z''=f(x,y,y')\) with one of the three classical pair of boundary conditions is reduced to an appropriate initial value problem and the straightforward determination of a parameter if (*) and a boundary condition are invariant under a stretching group of transformations. If (*) is invariant under the general spiral group it may be reduced to the preceding case. The class of problems where the method is applicable is clearly limited.