We will study the structure and implementation of certain specially formulated adaptive grid methods for computing the numerical solution of a class of degenerate semilinear combustion-quenching problems. The problems have important physical and engineering applications. Modified arc-length procedures are designed in the spatial and/or temporal directions for robust adjustments of the discretizations throughout our computation. Milne-alike device is introduced for estimating and control of the computational error. The numerical solution generated converges monotonically to the physical solution of the underlying problems up to the combustion-quenching point. Numerical examples are given for demonstrating our conclusions.

WHERE: TEC 251