  For the problem of solving Reynolds equation under natural boundary
conditions, the corresponding hypothetical solution can be obtained by assuming
the free boundary. If the solution satisfies natural boundary conditions, then
the boundary is the boundary we are looking for. Obviously, there is a set S
formed by all the boundaries that assume the solution is positive. We prove
equivalence between maximum element of S and natural condition. We prove the
closeness of set S under addition. Therefore, we prove that the set S must have
a unique greatest element. Furthermore, we obtain the uniqueness and existence
of solutions of Reynolds equation under natural boundary conditions.
  In engineering, the zero setting method is often used to find the boundary of
Reynolds equation, and we also give the proof that the zero setting method has
only one iterative error solution. We give an algorithm for solving Reynolds
equation under one-dimensional conditions, which reaches the theoretical upper
bound.
  We discuss the physical meaning of this method at the end.
