Euler Root Mean Square (ERMS): A New Modified Euler Method to Improve Accuracy of Resistor-Inductor (RL) Circuit Equation

Abstract Numerical method is a technique of obtaining the nearest approximation for the solution of various problems that can be described in the form of derivative equations. Engineering issues cannot be simply overcome using analytical concepts. This study aims to propose a new scheme from an enhanced Euler method for testing the resistor-inductor (RL) circuit equation. For this purpose, the paper proposes the Euler Root Mean Square (ERMS), a modified Euler method with improved accuracy. It will justify that the new scheme can be as accurate as possible in providing the exact solution by applying an average concept of using root mean square. It will focus on this accuracy by comparing the exact solution and actual solution between the new ERMS scheme and a modified Euler known as Euler Arithmetic. This study has demonstrated that the ERMS provided solutions that are similar to the exact solutions at t=0.5. It proves that an enhanced Euler method can be applied in various fields, especially in electrical engineering. In conclusion, the ERMS can be used as an alternative algorithm to solve RL circuit problems.