This paper analysed the Rosenweig-MacArthur model. The model simulates interaction between a type of prey and its predator. The aim was to analyses the performance of two famous and accurate method; i.e. Adam-Moultan and fourth order Runge-Kutta methods on the behavior of the Rosenweigh-MacArthur model. We also investigate the impact on eight mesh sizes on both methods. We also examine the effect of various sets of birth and death rate of prey and predators on the logical behaviour of simulated result. Results show that both methods simulate the problem with almost the same accuracy. Both methods have logically simulated the behaviour of prey and predator except for big mesh sizes but in term of computation time the Adam-Moultan method solve all problems faster than the fourth order Runge-Kutta method. © 2015 IEEE.