High accuracy difference schemes for the cylindrical heat conduction equation

High accuracy implicit difference methods including some unconditionally stable implicit formulas are derived for the cylindrical heat conduction equation. An implicit two-level formula of order (k square + h to the fourth) is derived, and, by use of the transformation suggested by Mitchell and Pearce (1963), a two-level implicit formula of the same order was obtained for integrating the transformed equation. The difference formulas and the Mitchell and Pearce explicit schemes were used to solve two example problems, and it is found that the implicit two-level formula is more advantageous.