A precise Runge–Kutta integration and its application for solving nonlinear dynamical systems

In this paper, precise integration is compounded with Runge–Kutta method and a new effective integration method is presented for solving nonlinear dynamical system. Arbitrary dynamical system can be expressed as nonhomogeneous linear differential equation problem. Precise integration is used to solve its corresponding homogeneous equation and Runge–Kutta methods can be used to calculate the nonhomogeneous, nonlinear items. The precise integration may have large time step and the time step of the Runge–Kutta methods can be adjusted to improve the computational precision. The handling technique in this paper not only avoids the matrix inversion but also improves the stability of the numerical method. Finally, the numerical examples are given to demonstrate the validity and effectiveness of the proposed method.