An adaptive grid method for degenerate semilinear quenching problems

This paper studies the structure and implementation of a specially formulated adaptive grid method for computing the numerical solution of a class of degenerate semilinear quenching problems. Modified arc-length procedures are used in both the space and time for robust adjustments of the spatial and temporal discretizations throughout the computation. A Milne-like device is introduced in the error estimation and control of the computational error. The numerical solution generated converges monotonically to the physical solution of the underlying problem up to the quenching time. Numerical examples are given for demonstrating our conclusions.