... advancedinterval methods (AIM) have been applied to evaluate the iteration formula (7), see Step 4, Section IV. InVNODE, an interval Taylor series method with QR factorization has been employed while for ... — for the initial conditions y0app,0= x0appand y0app, j= 0, ∀ j ≥ 1. Now, the iteration (7)is performed with the improved approximation xapp(t) for ε = 1 which is demonstrated for ... are quite general ideas, they can be employed for various enclosure methods, i.e., notonly for VALENCIA-IVP but also for methods like those from VNODE or COSY VI. Consistency testswhich are...