A numerical implementation of the alternating dimension algorithm for Tokamaks with ripple is presented. An explicit (Euler) method is used for the convective-diffusive system. The 1-D calculation is periodically interrupted for a new (3-D) equilibrium calculation. The transport system requires a small number of 'quasi-geometrical' coefficients obtained through the Bauer-Betancourt-Garabedian code (1978). Results are presented for the Braginskii classical transport model for the evolution of a high beta elongated Tokamak with high field ripple over the resistive skin time. The model is extended by adding the ripple-plateau coefficient for thermal diffusitivity which couples the field ripple with enhanced loss at high temperature. Preliminary results are presented for the ATE torsatron searching for the pressure and rotational transform evolution to an external current source.