THE EFFECTIVENESS OF THE NEW MODIFIED EULER METHOD

Authors

• Jutamas Tiensriphum Department of Mathematics Statistics and Computer, Faculty of Sciences, Ubonratchathani University.
• Jiratchaya Jaisaardsuetrong Department of Mathematics Statistics and Computer, Faculty of Sciences, Ubonratchathani University.

Keywords:

Consistency, Errors, Modified Euler's Method, Ordinary Differential Equations, Stability

Abstract

The purpose of this paper was to discover a new modified Euler method for solving ordinary differential equations that was the most efficient compared to the Euler’s method and Modified Euler methods, which were the classical methods. The new modified Euler method was developed by approximating solutions in the next intervals using three slopes in the present intervals. In addition, errors of Euler's method, modified Euler method, the new modified Euler method and the third-order Runge-Kutta method were compared. The stability and consistency of the new modified Euler method were proposed. When the new modified Euler method was compared to Euler's method, the Modified Euler method and the third-order Runge-Kutta method, the results revealed that the new modified Euler method exhibited superior effectiveness and lower error rates. However, in comparison with third-order Runge-Kutta method, the new modified Euler method exhibited higher errors due to the fact that the third-order Runge-Kutta method is highly efficient choice for approximating solutions of ordinary differential equation.

References

Rizky, A., Mochammad, A., Aji, P., and Sri, P. (2021). Comparison of numerical simulation of epidemiological model between euler method with 4th order runge kutta method. International Journal of Global Operations Research, 2, 37-44.

Ochoche, A. (2008). Improving the improved modified Euler's method for better performance on autonomous initial value problems. Leonardo Journal of Sciences, 12, 57-66.

Sampoornam, P. (2016). A study on numerical exact solution of Euler, improved Euler and Runge Kutta methods. International Journal of Novel Research in Physics Chemistry and Mathematics, 3(1), 1-5.

Mohd Yusop, N. M., Hasan, M. K., Wook, M., Mohamad Amran, M. F., and Ahmad, S. R. (2017). Comparison new algorithm modified euler based on harmonic-polygon approach for solving ordinary differential equation. Journal of Telecommunication, Electronic and Computer Engineering, 9(2-11), 29-32.

Ram, T., Solangi, A. M., and Asghar, A. (2020). A hybrid numerical method with greater efficiency for solving initial value problems. Mathematical Theory and Modeling, 10(2), 1-7.

Din Ide, N. A. (2022). Modification on euler-cauchy method for solving first-order differential equations. Asian Journal of Pure and Applied Mathematics, 4(1), 56-62.

Gilat, A., and Subramaniam, V. (2010). Numerical Methods (2nd ed.). John Wiley and sons, Inc.

2024-04-30

How to Cite

Tiensriphum, J., & Jaisaardsuetrong, J. (2024). THE EFFECTIVENESS OF THE NEW MODIFIED EULER METHOD. Srinakharinwirot University Journal of Sciences and Technology, 16(31, January-June), 1–13, Article 253650. Retrieved from https://ph02.tci-thaijo.org/index.php/swujournal/article/view/253650

บทความวิจัย