Module 5: Consistency, Stability and Convergence of General Single – Step Methods
  Lecture 15: Convergence of General One-Step Methods
 

 

Illustrative Example:

Let us now apply the above theorem to illustrate the convergence of Classical Runge-Kutta method applied to the system of first order equations .

We are given that satisfies a Lipschitz condition. Thus, satisfies

satisfies

satisfies

and satisfies