A linearized difference scheme for semilinear parabolic equations with nonlinear absorbing boundary conditions

A novel three level linearized difference scheme is proposed for the semilinear parabolic equation with nonlinear absorbing boundary conditions. The solution of this problem will blow up in finite time. Hence this difference scheme is coupled with an adaptive time step size, i.e., when the solution tends to infinity, the time step size will be smaller and smaller. Furthermore, the solvability, stability and convergence of the difference scheme are proved by the energy method. Numerical experiments are also given to demonstrate the theoretical second order convergence both in time and in space in L∞-norm.