THE EFFECTIVENESS OF THE NEW MODIFIED EULER METHOD - Tiensriphum, Jutamas; Jaisaardsuetrong, Jiratchaya (Srinakharinwirot University Journal of Sciences and Technology, 2024)
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.