Comparing Accuracy of Differential Equation Results between Runge-Kutta Fehlberg Methods and Adams-Moulton Methods

There are many issues in the fields of physics, chemistry, biology, and astronomy which can be solved through differential equation formulations. In general, the completion of differential equations can be done analytically or by numerical methods. If the completion is done analytically, usually it is done through calculus theories, and may require a longer time to solve. Anticipating the difficulties posed by differential equations analysis, numerical method is being used instead. This numerical completion provides solution in the form of approach and being carried out by visiting the initial value which then needs to be advanced gradually, step by step. Utilizing computers in solving differential equations would also help develop the application of numerical methods. Therefore, this study is expected to be able to improve the existing methods. This research will compare the accuracy of different methods, the Runge-Kutta Fehlberg and Adams-Moulton methods, in completing differential equations, which is limited to ordinary differential equations of first order and second order. It is found that there is general difference between the two method with Runge-Kutta Fehlberg method being the one-step method with an uncertain step size, while the Adams-Moulton method being the double steps method. Comparison of accuracy is obtained