The efficiency of implicit and semi-implicit time integration codes based on bac- kward differentiation and extrapolation formulae for the solution of the three-dimensio- nal Boussinesq thermal convection equations in rotating spherical shells is studied. The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storage requirements. The results show that high order methods, either with or without time step and order control, increase the efficiency of the time integrators, and allow to obtain more accurate solutions.

Peer Reviewed