Numerical methods for a singular boundary value problem with application to a heat conduction model in the human head

Proceedings of the 9th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2009), Vol. III (2009), 755-764
http://www.math.ist.utl.pt/~plima/papers/Proceedings/3.2.27.pdf

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.