Ulam Stability of a LCR Electric Circuit with Electromotive Force

Abstract

We enumerate the approximate solution of the second order differential equation of the LCR electric circuit. That is, we study the Hyers-Ulam stability and Hyers-Ulam-Rassias of the dirrential equations $ l''(t) + \dfrac{R}{L} \ l'(t) + \dfrac{1}{LC} \ l(t) = 0 $ and the non-homogeneous differential equation $ l''(t) + \dfrac{R}{L} \ l'(t) + \dfrac{1}{LC} \ l(t) = p(t)$, with initial conditions $ H(a) = H'(a) = 0$, where $R, L, C$ are constants and $l \in C^2 (I) $, $p(t) \in C(I)$, $I = [a, b] \subseteq \mathbb{R}$.