An implicit Douglas algorithm for a nonlinear singular quenching problem Original Research Article

A fourth-order iterative implicit algorithm is constructed for the approximate solution of a nonlinear parabolic partial differential equation up to its quenching time. The algorithm is particularly useful for long quenching times; sufficient conditions for its monotone convergence are derived. Numerical results using the new method are presented and compared with previous results obtained from a Crank-Nicolson algorithm.