Numerical Solution of the Integro-Differential Equation of the Transient Response in the Electric Circuits: Application of the Modified Euler's Method and Numerical Quadrature

Abstract

Integro-differencial equations plays an eminent role in description of various physical, chemical, and biological phenomena and systems, especially of a dynamic nature. They are used in construction of simulation models that try to mathematically solve the behavior and response of real events, occurring in diverse systems, completely or with a certain degree of approximation. Thus, it is of a high importance to solve them. However, in most cases, analytical approaches fail and therefore, numerical methods are necessary to employ to find their solution. In the present study, we focus on a problem of solving the integro-differential equation for the transient phenomena in a serial RLC circuit. We present a numerical method based on the explicit Euler protocol and compare its results with those from the analytical solutions in terms of the error development. These findings could stimulate future work, possibly exploiting other Runge-Kutta methods or multistep methods with different quadrature rules.