The method of fundamental solutions for non‐linear 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.