11. It is however possible to perform this integration numerically using the Runge Kutta method or similar techniques. 12. Examples of such routines are Euler's method, or better, the Runge Kutta methods . 13. All collocation methods are implicit Runge Kutta methods , but not all implicit Runge Kutta methods are collocation methods. 14. All collocation methods are implicit Runge Kutta methods, but not all implicit Runge Kutta methods are collocation methods. 15. Similar methods can be developed for higher order methods, such as the 4th order Runge-Kutta method . 16. I would like to model the evolution of \ cos \ theta, using the runge-kutta method . 17. The core of the simulation package is a variable step numerical integrator of fourth-order Runge-Kutta method . 18. A standard fourth-order Runge Kutta method is used for numerical integration of the ion trajectory in three dimensions. 19. Examples are Simpson's rule, the Runge Kutta method , and the Numerov algorithm for the Schr�dinger equation. 20. Explicit Runge Kutta methods have a strictly lower triangular coefficient matrix A and thus, their stability function is a polynomial.
