Comparison of Adams-Bashforth and Runge-Kutta methods of order 4 I have a system of ODE, that must to solve with numerical methods. I solve it by Adams_Bashforth with order4 and Runge-Kutta with order4 methods. Do you know with same length step which methods answers exactly?
Runge-Kutta is a fixed step solver but Adams is a variable step solver. You can't compare them with the same step size because in Adams method you define max. and min. step size with relative tolerance. You don't define a single step size like 0.01 as in Runge Kutta method. Obviously, variable step solvers give smoother results but the computation time also increases.

You can find a comparison of different methods here: Matlab Alghorithms

Edit: This answer is about variable step Adams-Bashforth-Moulton solver in Matlab. I don't know its fixed step version.
Runge-Kutta is a fixed step solver but Adams is a variable step solver. You can't compare them with the same step size because in Adams method you define max. and min. step size with relative tolerance. You don't define a single step size like 0.01 as in Runge Kutta method. Obviously, variable step solvers give smoother results but the computation time also increases.

You can find a comparison of different methods here: Matlab Alghorithms

Edit: This answer is about variable step Adams-Bashforth-Moulton solver in Matlab. I don't know its fixed step version.