Ulam-Hyers Stability of Second-Order Convergent Finite Difference Scheme for First- and Second-Order Nonhomogeneous Linear Differential Equations with Constant Coefficients

This article studies the Ulam-Hyers stability of the secondorder convergent finite difference scheme for the first- and second-order non-homogeneous linear differential equations x'(t) - bx(t) = f(t) and x ''(t) + ax'(t) + beta x(t) = g(t), on the interval I = [a, infinity), respectively, where f.g : I -> R are given functions and alpha, b, alpha, beta is an element of R. After converting the finite difference scheme to its equivalent linear recurrence relation and by using the Ulam-Hyers stability results for the linear recurrence relation, we establish the Ulam-Hyers stability for the finite difference scheme. Further, as per the location of the roots of the characteristic polynomial of the equivalent recurrence relation, the minimum UlamHyers constant is determined. To illustrate the utility of the obtained result, we apply our result to the perturbed second-order nonlinear difference equation and present a suitable example at the end to support the obtained result.