A class of singular boundary value problems modeling the heat conduction in the human head is studied. Suitable singular Cauchy problems are considered in order to determine one parameter families of solutions in the neighborhood of the singularities. These families are then used to construct stable shooting algorithms to the solution of the considered problems. A finite difference method is also introduced and, taking into account the behavior of the solution in the neighborhood of the singular points, a variable substitution is proposed to improve its convergence order. Numerical results are presented and discussed.

CEMAT - Center for Computational and Stochastic Mathematics