Abstract: In this paper, we introduce a method for improving
the embedded Runge-Kutta-Fehlberg4(5) method. At each integration
step, the proposed method is comprised of two equations for the
solution and the error, respectively. These solution and error are
obtained by solving an initial value problem whose solution has the
information of the error at each integration step. The constructed algorithm
controls both the error and the time step size simultaneously and
possesses a good performance in the computational cost compared to
the original method. For the assessment of the effectiveness, EULR
problem is numerically solved.