granular media of CoCrPtTa structure (type a) and micromagnetic standard problem #4 has been done. Moreover, an investigation of the effect of the maximum dimension of the Krylov subspace projection methods, within the Ordinary Differential Equations (ODEs) context, on the speed of micromagnetic simulations on granular media of Co structure (type b) has been done. The stiffness of the problems has been investigated using two different solvers, a non-stiff (Adams) and a stiff one (backward differentiation formulae, BDF) for the solution of the large system of ODEs. The results show that granular media (type a) micromagnetic simulations are stiff, whereas µ MAG standard problem #4 is not. Furthermore, it has been found that increasing the maximum dimension of the Krylov subspace to 20 (default value =5) a considerable increase to the speed of the granular media simulations occurs in the order of approximately 90%.