Module 5: Consistency, Stability and Convergence of General Single – Step Methods
Lecture 15: Convergence of General One-Step Methods
Therefore,
satisfies
Hence satisfies a Lipschitz condition in . It can also be seen to be continuous in . Thus we can conclude that the classical fourth order Runge-Kutta method converges for a system of equations.
satisfies 
satisfies a Lipschitz condition in 
. It can also be seen to be continuous in 
. Thus we can conclude that the classical fourth order Runge-Kutta method converges for a system of equations. 
