An Interval Version of the Crank-Nicolson Method - The First Approach

To study the heat or diffusion equation it is often used the Crank-Nicolson method which is unconditionally stable and has order of convergence O(k + h ), where k and h are mesh con2 2 stants. Unfortunately, using this method in conventional floatingpoint arithmetic we get solutions including not only the method error, but also representation and rounding error, Therefore, we propose an interval version of Crank-Nicolson method from which we would like to obtain solutions including the method error. Applying such a method in interval floating-point arithmetic one can get solutions including all possible numerical errors. A numerical example is presented.