A survey on the Liouville-Green (WKB) approximation for linear difference equation of the second order.

*(English)* Zbl 0892.39018
Elaydi, S. (ed.) et al., Advances in difference equations. Proceedings of the 2nd international conference on difference equations, Veszprém, Hungary, August 7–11, 1995. Langhorne, PA: Gordon and Breach Science Publishers. 567-577 (1997).

Summary: The main results concerning the Liouville-Green (WKB) approximation for second-order linear difference equations are reviewed. This is an asymptotic representation of a special type (other than power series) for solutions, where precise error bounds accompany the approximation, and was earlier introduced only formally, mostly by physicists, as in the continuous case. Rigorous results have been given more recently and are described along with several applications.

##### MSC:

39A12 | Discrete version of topics in analysis |

39A10 | Additive difference equations |

34E20 | Asymptotic singular perturbations, turning point theory, WKB methods (ODE) |