High accuracy difference schemes for a class of three space dimensional singular parabolic equations with variable coefficients

In this article, two-level implicit difference methods of O(k2 + h4) using 19-spatial grid points for the solution of three space dimensional heat conduction equation and unsteady Navier-Stokesʹ equations in polar coordinates are proposed. Unconditionally stable ADI methods for the solution of the heat conduction equation in polar coordinates are also discussed. Numerical examples given here show that the methods developed here retain their order and accuracy everywhere including the region in the vicinity of the singularity r = 0.