The comparison of runge-kutta and adams-bashforh-moulton methods for the first order ordinary differential equations

Abstract

The performances of Runge-Kutta and Adams-Bashforth-Moulton methods were compared by considering first order ordinary differential equations using the MATLAB software. For this purpose three major programs were coded for RK4, ABM, and MABM and run using the MATLAB software. This is done by varying the step length M and sketching graphs of computation time. For the comparison of accuracy, relative errors have been calculated for each first order ordinary differential equations and represented by graphs. Moreover the effectiveness of modifiers in the Adams-Bashforth-Moulton 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 among RK4, ABM, and MABM. 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. 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 but this doesn’t work for some problems due to the stiffness of the problem and instability of the modifier in the corrector step. Future experiments can be done by increasing the types of numerical methods and extending the first order ODEs in to higher order.