High order difference methods for heat equation in polar cylindrical coordinates

Abstract

Fourth-order difference methods for the solution of Poisson equations in cylindrical polar coordinates are proposed. The same technique is then applied to obtain O( k 2 + h 4), two level, unconditionally stable ADI methods for the solution of the heat equation in two-dimensional polar coordinates and three-dimensional cylindrical coordinates. 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.