A Comparative Study on the Numerical Simulation of Ordinary Differential Equation with Euler and higher Order Taylor’s Methods

The two primary approaches presented in this work for solving initial value problems for ordinary differential equations are the Euler technique and the Higher Order Taylor’s technique. Both of the suggested approaches are practically effective and suitable for addressing these issues. We evaluate numerical results with exact solutions to confirm accuracy. The exact solutions and the numerical solutions show good agreement. The Higher Order Taylor’s Method and the Euler Method are numerically compared. We assess the efficiency of these approaches as well as their computational effort. The step size must be extremely small to achieve higher accuracy in the solution. We investigate and compute the errors of the two suggested approaches for various step sizes, and then evaluate their superiority. To demonstrate their dependability and effectiveness, several numerical examples are provided.