Error Analysis in Numerical Techniques Using Euler's Method with a Practical Application

Bevreen Rashid  Ali

Bevreen Rashid Ali Qalawlis Education, Islamic Azad University, Iran

Keywords: differential calculus, fractional integration, logistics equation, fractional logistic equation, matlab

Abstract

The objective of this study is to apply Euler's method to simulate the dynamics of infectious disease spread using the SIR (Susceptible-Infectious-Recovered) model. By utilizing Euler's method, this research aims to numerically approximate the solutions to the differential equations governing the spread of the disease within a population. This simulation allows for the analysis of changes in the populations of susceptible, infectious, and recovered individuals over time, as well as the influence of parameters such as transmission and recovery rates. The methodology involves the application of both explicit and implicit Euler methods to solve first-order differential equations. Simulations were conducted using MATLAB to analyze the accuracy and errors that arise during the numerical computation process. The results indicate that Euler's method, while simple and easy to implement, has limitations in terms of accuracy, particularly when larger time steps are used. The errors tend to increase over time, which can affect the validity of the simulation results. The SIR model simulation demonstrates how a disease spreads within a population and highlights the importance of considering appropriate parameters for effectively controlling and managing outbreaks.

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