Analysis of solution methods for high order ordinary differential equations used inelectrical circuits

This article presents a detailed methodology for applying the most common methods in solving high-order ordinary differential equations in the simulation of electrical circuits. The methods analyzed include the Laplace transform, the direct method in the time domain, the z-transform, the finite difference method, and methods based on difference equations. A detailed development of each of these methods is provided, along with practical examples that demonstrate their application in specific electrical circuits. The examples include: a circuit modeled with a second-order ordinary differential equation, a circuit modeled with a third-order ordinary differential equation, and an electrical network whose modeling results in an eighth-order ordinary differential equation. The article compares the results obtained with each method, using the Laplace transform solution as a reference. A deep analysis of the deviations between the methods is conducted, considering different time steps and parameters, allowing conclusions to be drawn about the effectiveness and accuracy of each approach.