Nonlinear moving boundary problems and a Keller box scheme. (English) Zbl 0558.65087

Meek, Peter C.; Norbury, John

SIAM J. Numer. Anal. 21, 883-893 (1984).

Authors’ summary: A modification of the original Keller box scheme is used to approximate nonlinear parabolic 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.

Reviewer: U.Hornung

MSC:

65Z05	Applications to the sciences
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35R35	Free boundary problems for PDEs

Keywords:

nonlinear diffusion equation; Stefan problem; Keller box scheme; moving boundary; comparison of numerical results; similarity solution; stability; convergence