Highly accurate family of time integration method

In this study, the acceleration vector in each time step is assumed to be a mth order time polynomial. By using the initial conditions, satisfying the equation of motion at both ends of the time step and minimizing the square of the residual vector, the m+3 unknown coefficients are determined. The order of accuracy for this approach is m+1, and it has a very low dispersion error. Moreover, the period error of the new technique is almost zero, and it is considerably smaller than the members of the Newmark method. The proposed scheme has an appropriate domain of stability, which is greater than that of the central difference and linear acceleration techniques. The numerical tests highlight the improved performance of the new algorithm over the fourth-order Runge-Kutta, central difference, linear and average acceleration methods.