Nonlinear Moving Boundary Problems and a Keller Box Scheme

A modification of the original Kelley box scheme is used to approximate nonlinear parabolic partial differential equations with moving boundaries. The proposed scheme solves two systems of linear algebraic equations at each time-step to produce second-order approximations to the solution, its derivative (the flux) and the position of the moving boundary. The scheme is applied to a physical problem which has a known similarity solution. A comparison of numerical results with the similarity solution gives evidence of stability and convergence.