Singularly perturbed difference equations

Comstock and Hsiao have given a method for constructing asymptotic approximations for singularly perturbed linear difference equations with two point boundary conditions and for verifying the correctness of the approximation. We present a general method for construction and verification of asymptotic approximations for the nonlinear equation f(t, is an element of y(t - 1), y(t), y(t + 1), is an element of) = 0, where \is an element of\ is a small parameter, with either initial or boundary conditions. The technique is easily extended to more general problems.