For the abstract initial value problem describing by the equations \[ u'(t)= Au(t)+ f(t),\quad 0\leq t\leq T,\qquad u(0)= u_0, \] where \(A: D(A)\subset X\to X\) is a infinite-dimensional generator of a \(C_0\)-semigroup in a Banach space \(X\), \(f:\langle 0,T\rangle\to X\) and \(u_0\in X\). A new strategy of the Runge-Kutta method is proposed. The aim of this strategy is to avoid the order reduction during the solution of the given linear, autonomous, nonhomogeneous initial boundary value problem, which occurs in many evolutionary problems of practical interest, either hyperbolic or parabolic types. The proposed solution process is decomposed into two steps. The first can be computed directly in terms of the data, the second satisfies an initial value problem without any order reduction. A numerical illustration is given. This idea can be applied to practical problems, where a spatial discretization is also required, leading to full order both in space and in time.