  An efficient numerical scheme for solving transport equations for tokamak
plasmas within an integrated modelling framework is presented. The plasma
transport equations are formulated as diffusion-advection equations in two
coordinates (a temporal and a spatial) featuring stiff non-linearities. The
presented numerical scheme aims to minimise computational costs, which are
associated with repeated calls of numerically expensive physical models in a
processes of time stepping and non-linear convergence within an integrated
modelling framework. The spatial discretisation is based on the 4th order
accurate Interpolated Differential Operator in Conservative Formulation, the
time-stepping method is the 2nd order accurate implicit Runge-Kutta scheme, and
an under-relaxed Picard iteration is used for accelerating non-linear
convergence. Temporal and spatial accuracies of the scheme allow for coarse
grids, and the implicit time-stepping method together with the non-linear
convergence approach contributes to robust and fast non-linear convergence. The
spatial discretisation method enforces conservation in spatial coordinate up to
the machine precision. The numerical scheme demonstrates accurate, stable and
fast non-linear convergence in numerical tests using analytical stiff transport
model. In particular, the 2nd order accuracy in time stepping significantly
improves the overall convergence properties and the accuracy of simulating
transient processes in comparison to the 1st order schemes.
