This paper describes numerical experiments made to investigate the stability of some time-stepping algorithms applied to the equation ii + P(u) = 0 representing a nonliner elastic spring. These algorithms would be unconditionally stable when applied to linear problems, but here they may be only conditionally stable. Ways of improving the stability are demonstrated; the effect of linearization is also investigated.

This study has come up with a numerical scheme that arises from finite volume discretizationof Modified Navier-Stokes Equation.Modified Navier-Stokes Equation in the x-z axis was coupled with continuity equation to obtain the Pressure Equation. Using the pressure equation, pressure field can bedetermined in each control volume on a staggered grid.