ZERO-STABILITY AND CONVERGENCE FOR INITIAL VALUE PROBLEMS (CAHIERS MAGELLANES-NS, 2024)
Within this research, we worked on the concepts of zero stability and convergence for initial value problems via numerical methods, and the primary goal was to analyze the convergence properties of one-step methods, with a direct and special focus on Euler’s method, within the field of linear problems, as this paper that we conducted investigates error.  Local truncation and the global error of Euler's method, in order to extract ideas about its accuracy and asymptotic behavior, where a general error term is derived based on the maximum local truncation error and the size of the time step, while mentioning some studies that develop a broader analysis of other one-step methods and nonlinear problems, and through these results we arrive at  To a deeper understanding of numerical methods for initial value problems  thereby paving the way for further research and progress in this field.