Comparative Study on Results of Euler, Improved Euler and Runge-Kutta Methods for Solving the Engineering Unknown Problems

Abstract

The paper presents the comparative study on numerical methods of Euler method, Improved Euler method and fourth-order Runge-Kutta method for solving the engineering problems and applications. The three proposed methods are quite efficient and practically well suited for solving the unknown engineering problems. This paper aims to enhance the teaching and learning quality of teachers and students for various levels. At each point of the interval, the value of y is calculated and compared with its exact value at that point. The next interesting point is the observation of error from those methods. Error in the value of y is the difference between calculated and exact value. A mathematical equation which relates various functions with its derivatives is known as a differential equation. It is a popular field of mathematics because of its application to real-world problems. To calculate the exact values, the approximate values and the errors, the numerical tool such as MATLAB is appropriate for observing the results. This paper mainly concentrates on identifying the method which provides more accurate results. Then the analytical results and calculates their corresponding error were compared in details. The minimum error directly reflected to realize the best method from different numerical methods. According to the analyses from those three approaches, we observed that only the error is nominal for the fourth-order Runge-Kutta method.