# Simple use of the Maclaurin series method for linear and non-linear differential equations arising in circuit analysis

Yasir Khan (Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin, Saudi Arabia, and)
Naeem Faraz (International Cultural Exchange School, Donghua University, Shanghai, China)

ISSN: 0332-1649

Article publication date: 7 August 2021

Issue publication date: 20 August 2021

41

## Abstract

### Purpose

The purpose of this paper is to investigate the circuit analysis differential equations, which play an important role in the field of electrical and electronic engineering, and it was necessary to propose a very simple and direct method to obtain approximate solutions for the linear or non-linear differential equations, which should be simple for engineers to understand.

### Design/methodology/approach

This paper introduces a simple novel Maclaurin series method (MSM) to propose an approximate novel solution in the area of circuit analysis for linear and non-linear differential equations. These equations describe the alternating current circuit of the resistor–capacitor, which evaluates the effect of non-linear current resistance. Linear and non-linear differential equations are evaluated as a computational analysis to assist the research, which reveals that the MSM is incredibly simple and effective.

### Findings

Simulation findings indicate that the achieved proposed solution using the novel suggested approach is identical to the exact solutions mentioned in the literature. As the Maclaurin series is available to all non-mathematicians, this paper reflects mostly on theoretical implementations of the numerous circuit problems that occur in the field of electrical engineering.

### Originality/value

A very simple and efficient method has been proposed in this paper, which is very easy to understand for even non-mathematicians such as engineers. The paper introduced a method of the Maclaurin series to solve non-linear differential equations resulting from the study of the circuits. The MSM mentioned here will be a useful tool in areas of physical and engineering anywhere the problem of the circuits is studied.

## Acknowledgements

The authors are grateful to the referees, whose comments and suggestions improved the presentation and value of the article. The authors extend their appreciation to the Deanship of Scientific Research, University of Hafr Al-Batin for funding this work through the research group project no. (G-108-2020).

## Citation

Khan, Y. and Faraz, N. (2021), "Simple use of the Maclaurin series method for linear and non-linear differential equations arising in circuit analysis", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 40 No. 3, pp. 593-601. https://doi.org/10.1108/COMPEL-08-2020-0286

## Publisher

:

Emerald Publishing Limited