The performances of Runge-Kutta (RK4) and Adams-Bashforth-Moulton(ABM) methods were compared by considering first order ordinary differential equations. Moreover the effectiveness of modifiers in the ABM method has been validated. The result of this research show that ABM method is the most efficient method for first order ODE but in terms of accuracy there is no one best method. So it is not possible to make generalizations. But it is possible to conclude that the performance of a given method depend on the characteristics of the ODEs we are considering such as stiffness and stability. Regarding the modifiers in the corrector and predictor formulas of the ABM method, they are effective in improving the accuracy of ABM method in most cases.
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