...Suying Zhang; Jiangdan Li The precise integration method can give precise numerical result for linear invariant dynamical system, and can be used to solve stiff linear invariant dynamical system. In this paper, precise integration is compounded with Runge–Kutta method and a new effective...

...Junyi Cao; Chengbin Ma; Hang Xie; Zhuangde Jiang In this paper, nonlinear dynamics of Duffing system with fractional order damping is investigated. The fourth-order Runge–Kutta method and tenth-order CFE-Euler method are introduced to simulate the fractional order Duffing equations. The effect...

... Newton method Runge-Kutta methods shear modulus sparse matrices The implementation of multistage implicit integrators requires the solution of nonlinear algebraic equations. This is one of the most time-consuming aspects of the integration process. Newton’s iterative method, or a modified...

... with Newmark’s method and the fourth-order Runge–Kutta (Kutta 4) method are presented. The examples demonstrate the high accuracy and numerical efficiency of the proposed method. nonlinear dynamical systems numerical analysis polynomial approximation Runge-Kutta methods nonlinear dynamics time...

... with LuGre friction. Several simulation strategies are applied including the explicit Runge–Kutta, implicit Trapezoidal, and implicit Radau-IIA schemes. It was found that both the Runge–Kutta and Radau-IIA methods performed well in simulating the system. The Runge–Kutta method had better accuracy...

... to ordinary differential equations (Cauchy problem) is carried out using the higher order Bubnov–Galerkin’s approach and Fourier’s representation. On the other hand, the Cauchy problem is solved using the fourth-order Runge–Kutta method. Results are analyzed owing to the application of nonlinear dynamics...