A Second-Order Scheme for Nonlinear Fractional Oscillators Based on Newmark-beta Algorithm

作者：Liu, Q X; Liu, J K; Chen, Y M^*

来源：Journal of Computational and Nonlinear Dynamics, 2018, 13(8): 084501.

DOI：10.1115/1.4040342

• fractional derivative
• nonlinear oscillator
• Volterra integral equation
• Newmark-beta method

This paper presents an accurate and efficient hybrid solution method, based on Newmark-b algorithm, for solving nonlinear oscillators containing fractional derivatives (FDs) of arbitrary order. Basically, this method employs a quadrature method and the Newmark-beta algorithm to handle FDs and integer derivatives, respectively. To reduce the computational burden, the proposed approach provides a strategy to avoid nonlinear algebraic equations arising routinely in the Newmark-beta algorithm. Numerical results show that the presented method has second-order accuracy. Importantly, it can be applied to both linear and nonlinear oscillators with FDs of arbitrary order, without losing any precision and efficiency.

• 出版日期2018-8
• 单位中山大学