Numerical method for singularly perturbed differential-difference equations with turning point (Q2893030)

Some a priori estimates are obtained for the solution and its derivatives of second order two-point boundary value problems associated to singularly perturbed differential-difference equations with turning point on [-1,1]. A numerical method based on the exponential box scheme of \textit{T. M. El-Mistikawy} and \textit{M. J. Werle} [AIAA J. 16, 749--751 (1978; Zbl 0383.76018)], on a uniform grid of [-1,1] is proposed to solve such type singularly perturbed differential-difference equations with turning point. The convergence and the stability of the proposed method are proved by obtaining some a priori error estimates. Two test numerical examples are presented in order to illustrate the accuracy of the method.