Hyers–Ulam Stability of a Second-Order Finite Difference Scheme Using a Diamond-\(\alpha \) Difference Operator

We establish the Hyers–Ulam stability of a second-order finite difference scheme using a diamond- \(\alpha \) $\alpha$ difference operator for second-order non-homogeneous linear differential equations with constant coefficients. Hyers–Ulam stability constants and best stability constants are determined for stability regions in the parameter space. In an application of our results, we compare our difference scheme with the more common centered-difference scheme, as an approximation to secord-order differential equations.