Comparative Analysis of Adams-Bashforth-Moulton and Runge-Kutta Methods for Solving Ordinary Differential Equations Using MATLAB

Abstract

This study deals with ordinary differential equations and their solutions consuming effective numerical methods. We observing for more accurate numerical methods proximate to MATLAB solutions. Approaches are Adams-Bashforth and Rung-Kutta-4 ought very good solutions, in the first response with ordinary differential equations of the primary order. Similarly, evaluation of modified second order numerical answers using, MATLAB and Adams-Bashfort-Moulton, by differential equation addition to numerical modeling methods expending fourth-order Runge-Kutta yielded excellent results. For the reason that the solutions are validated with high credibility, we explored in turn to best approximation results computed for the purpose of correcting them. Objective of new approach of this study was illustrated clear picture thru solving two examples with different numerical approximation methods. Compared are clearly shown in tables and figures to determine effectiveness and choose the best accuracy. We calculated different performance indices for several numerical methods using MATLAB and Moulton which yielded an excellent approximation through exams. We recommend it to be widely used in the future, and strive to develop it with faster and more accurate solutions.