In this paper, we present a numerical approach to a class of
nonlinear reaction-diffusion equations with nonlocal Robin type
boundary conditions by finite difference methods. A second-order
accurate difference scheme is derived by the method of reduction of
order. Moreover, we prove that the scheme is uniquely solvable and
convergent with the convergence rate of order two in a discrete
$L_2$-norm. A simple numerical example is given to illustrate the
efficiency of the proposed method.