A difference scheme for a parabolic system modelling the thermoelastic contacts of two rods

In this article, we study a sequence of finite difference approximate solutions to a parabolic system, which models two dissimilar rods that each rod is fixed at one end and is free to expand or contact at the other end. A finite difference scheme is derived by the method of reduction of order on nonuniform mesh. The unique solvability, unconditional stability, and convergence of the difference scheme are proved. The convergence order is of order two in both time and space. The convergence of iterative algorithm for the difference scheme are also discussed. A numerical example is presented to demonstrate the theoretical results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007