THE METHOD OF FUNDAMENTAL-SOLUTIONS FOR NONLINEAR THERMAL EXPLOSIONS

A numerical method based on the method of fundamental solutions, thin plate spine interpolation and monotone iteration is devised to find the minimal solution of the steady-state blow-up problem. The method of fundamental solutions requires neither domain nor boundary discretization and results in high accuracy and efficiency. For illustration, critical values of the Frank-Kamenetskii parameter are given for different geometrical boundaries in the two-dimensional case.