00, In this paper, an explicit family with higher-order of accuracy is proposed for linear and nonlinear dynamic analyses of structural and mechanical systems. In this paper, by using Taylor series, the amplification matrix of analytical solution is expanded, and by solving a system of nonlinear algebraic equations, coefficients required (α) for each stage of Runge-Kutta family are obtained. One of the superiorities of the proposed Runge-Kutta family is the equality between its order of accuracy, and the number of stages used in a single time step. As a weak point, the stability of the proposed family is conditional, so that the stability domain of the fourth-order Runge-Kutta method is larger than the first three orders of the proposed family (i.e. 5, 6, and 7). However, As a positive point, the order of accuracy of the family boosts by increasing the family order. As another positive point, any arbitrary order of the family can be easily achieved by solving a system of algebraic equations. The results illustrate that the suggested family is capable of analyzing various nonlinear systems with many degrees of freedom. Also, the proposed family achieves accurate results in analyzing tall building structures.

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