An Analysis of the Method of Lines for the Reynolds Equation in Hydrodynamic Lubrication

The Reynolds equation for a hydrodynamic journal bearing is discretized with the method of lines. A continuous analogue of the line SOR iteration is set up to solve the resulting free multipoint system of ordinary differential equations via a sequence of one-dimensional free boundary problems. It is shown that each one-dimensional problem can be solved with invariant imbedding, that the line SOR method converges, and that the solution of the by-lines discretization converges to the solution of a variational inequality derived from the Reynolds equation