This paper deals with the numerical study of a nonlinear, strongly anisotropic heat
equation. The use of standard schemes in this situation leads to poor results, due to the
high anisotropy. An Asymptotic-Preserving method is introduced in this paper, which is
second-order accurate in both, temporal and spacial variables. The discretization in time
is done using an L-stable Runge−Kutta scheme. The convergence of the method is shown to be
independent of the anisotropy parameter , and
this for fixed coarse Cartesian grids and for variable anisotropy directions. The context
of this work are magnetically confined fusion plasmas.