ANALYTICAL INVESTIGATION OF TWO-MESH CIRCUIT DYNAMICS USING ADOMIAN’S DECOMPOSITION APPROACH

Abstract

The Adomian Decomposition Method (ADM) serves as a powerful analytical technique for addressing both linear and nonlinear differential equations frequently encountered in engineering and applied science problems. In this study, ADM is employed to investigate two-mesh and two-loop electrical circuits characterized by first-order differential equations. By systematically applying Kirchhoff’s voltage and current laws, the loop current equations are derived and solved using a recursive decomposition process. The proposed method eliminates the need for numerical discretization or linearization, offering compact analytical expressions for voltage and current responses. The graphical analysis illustrates both transient and steady-state behaviors of the circuits, exhibiting strong consistency with theoretical expectations. The findings demonstrate that ADM is an efficient, accurate, and straightforward approach for modeling the dynamic performance of electrical circuits. Moreover, the technique can be effectively extended to the analysis of nonlinear, fractional-order, and thermoelectric systems.