In this paper, we study general polynomial discretizations in backward and forward looking, and the preservation of stability properties. We apply these results to the Ramsey model . Its discrete-time version is a hybrid discretizations of a backward-looking budget constraint and a forward-looking Euler equation. Saddle-path stability is a robust property under discretization.
H. Krivine, A. Lesne and J. Treiner, “Discrete-Time and Con-tinuous-Time Modelling: Some Bridges and Gaps,” Mathe-matical Structures in Computer Science, Vol. 17, No. 2, 2007, pp. 261-276.