Two new Runge–Kutta (RK) pairs of orders 6(4) and 7(5) are presented for solving numerically the inhomogeneous linear initial value problems with constant coefficients. These new pairs use only six and eight stages per step respectively. Six stages are needed for conventional Runge–Kutta pairs of orders 5(4) while for such a pair of orders 6(5) we use eight stages. Thus, our proposal is an improvement and it is achieved since the set of order conditions is smaller in the case of interest here. Since traditional simplifications for derivation of Runge–Kutta methods do not apply for this reduced set, we proceed using the differential evolution technique for solving it. We finalize by performing tests over some relevant problems with very pleasant results.

提出了两个新的阶为6（4）和7（5）的龙格－库塔（RK）对，用于数值求解常数系数不均匀的线性初值问题。这些新对每步仅使用六个和八个阶段。传统的Runge–Kutta订单5（4）对需要六个阶段，而对于这样的订单6（5）对我们则使用八个阶段。因此，我们的建议是一种改进，并且由于在这里感兴趣的情况下订单条件的集合较小而得以实现。由于Runge-Kutta方法推导的传统简化不适用于该简化集，因此我们使用差分进化技术进行求解。我们通过对一些相关问题进行测试来完成最终结果，结果非常令人满意。