Improving Euler Method using Centroidal-Polygon Scheme for Better Accuracy in Resistor-Capacitor Circuit Equation

Abstract

A first-order ordinary differential equation (ODE) is a function with two variables defined in the xy-axis of a field. Various numerical methods, such as the Euler method, Runge-Kutta method, Heun’s method and others, are used to solve ODEs, with varying computational costs and accuracy. The Euler method can only solve the first derivative equation with the simplest implementation at the lowest cost of computation, but it produces less accurate results. This research focuses on improving the Euler method to increase its accuracy. A new scheme called Centroidal-Polygon (CP) is used in this study. The CP scheme is tested on the Resistor-Capacitor (RC) circuit equation to ensure that it can be used in fields other than mathematics and computation. The RC circuit equation is used to compute maximum error and assess the accuracy of the CP scheme and its counterparts. The circuit equation’s accuracy in the RC circuit equation is determined by the time constant (τ). This research used Scilab 6.0 software to analyze the maximum error. The performance of the CP scheme was compared to the Polygon, Harmonic-Polygon, and Cube-Polygon schemes, which are all enhanced Euler methods. The results show that the CP scheme achieves higher accuracy while requiring less computing time. In future studies, the CP scheme will be applied to the RCL circuit equation and second-order ODE to ensure the CP scheme can be used in all applications.

Adaptive Fast Image Encryption Algorithm Based on Three-Dimensional Chaotic System

“…The use of the Euler algorithm may lead to degradation of chaos. An improved Euler algorithm can effectively improve the computational accuracy [47,48]. In this paper, the improved Euler algorithm is adopted to discretize the system (1).…”