High accuracy difference schemes for the cylindrical heat conduction equation
Abstract
High accuracy implicit difference methods including some unconditionally stable implicit formulas are derived for the cylindrical heat conduction equation. An implicit twolevel formula of order (k square + h to the fourth) is derived, and, by use of the transformation suggested by Mitchell and Pearce (1963), a twolevel 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 twolevel formula is more advantageous.
 Publication:

Journal of the Institute of Mathematics and Its Applications
 Pub Date:
 November 1978
 Bibcode:
 1978JIMIA..22..321I
 Keywords:

 Conductive Heat Transfer;
 Finite Difference Theory;
 Accuracy;
 Cylindrical Bodies;
 Numerical Stability;
 Fluid Mechanics and Heat Transfer