Transient Analysis of Electrical RLC Circuits Using a Variable-Step Variable-Order 2-Point Diagonal Block Backward Differentiation Formula

Abstract

Electrical circuits often experience transient phenomena when subjected to sudden changes, such as source switching, interruptions, or short circuits. These transients are particularly evident in RLC circuits, which may appear in series, parallel, or mixed configurations. The main challenge addressed in this study is the accurate and computationally efficient numerical solution of the rapid transient responses in second order RLC circuit models, particularly under different damping conditions. Accurate analysis of voltage and current fluctuations during these events is essential to understand transient behaviour and prevent potential damage to circuit components. This study focuses on the transient analysis of a second order RLC circuit using a variable-step variable-order 2-point diagonal block backward differentiation formula (VSVO 2DBBDF). The method directly solves the governing second order ordinary differential equations and adaptively adjusts the step size and order based on the local truncation error. The numerical results confirm that the proposed method is effective in capturing the transient behaviours in both series and parallel RLC circuits under underdamped, critically damped, and overdamped condition.

The authors' abstract, as published at the source. Journal of Engineering Research, 2026 · DOI ↗