  We introduce a computational method in physics that goes "beyond linear use
of equation superposition" (BLUES). A BLUES function is defined as a solution
of a nonlinear differential equation (DE) with a delta source that is at the
same time a Green's function for a related linear DE. For an arbitrary source,
the BLUES function can be used to construct an exact solution to the nonlinear
DE with a different, but related source. Alternatively, the BLUES function can
be used to construct an approximate piecewise analytical solution to the
nonlinear DE with an arbitrary source. For this alternative use the related
linear DE need not be known. The method is illustrated in a few examples using
analytical calculations and numerical computations. Areas for further
applications are suggested.
