Using MAPLE for the analysis of bifurcation phenomena in condensed-phase surface combustion

This article describes the use of the symbolic manipulation language MAPLE for the analysis of bifurcation phenomena in condensed-phase combustion. The physical problem concerns the structure and stability properties of a combustion front that propagates in the axial direction along the surface of a cylindrical solid fuel element. Experimental observations suggest that the front may propagate in a number of different ways; the objective of the investigation is to describe these different modes of propagation. The analysis involves the study of a set of nonlinear partial differential equations which describe the structure and evolution of the combustion front. Because the location of the front is unknown and must be found as part of the solution, the problem is a free boundary value problem. The purpose of this article is to show how symbolic manipulation languages like MAPLE can be combined effectively with analysis and numerical computations for this type of investigation.