On Ulam stability of a second order linear difference equation

Abstract

In this paper we obtain some Ulam stability results for the second order and the third order linear difference equation with nonconstant coefficients in a Banach space. The main idea of the approach is to decompose the second order linear difference equation in a Riccati difference equation and a first order difference equation. In this way we extend some results for linear difference equations with constant coefficients and for linear difference equations with periodic coefficients.

Keywords

• ulam stability
• approximate solution
• linear difference equation
• riccati difference equation
• nonconstant coefficients