On one generalization of Runge–Kutta method

There are offered to select the coefficients of one Runge–Kutta method generalization with regard to the value of relative error for linearized system of ordinary differential equations. Unlike the known versions of Runge–Kutta methods it is lead to Pade approximation not in zero, but in point nearest the spectrum of multiplied to mesh width the Jacobi matrix in the current mesh point.