Hyers–Ulam–Rassias Stability of Hermite’s Differential Equation

Abstract

In this paper, we studied the Hyers–Ulam–Rassias stability of Hermite’s differential equation, using Pachpatte’s inequality. We compared our results with those obtained by Blaga et al. Our estimation for zx−yx, where z is an approximate solution and y is an exact solution of Hermite’s equation, was better than that obtained by the authors previously mentioned, in some parts of the domain, especially in a neighborhood of the origin.

Keywords

• Hermite’s differential equation
• Hyers–Ulam–Rassias stability
• Pachpatte’s inequality