A Finite Difference Method for Positive Definite Fractional Damped String Vibration Equations

Congcong Wei, Zhe Yin and Ailing Zhu

Journal of Mathematics Research, 2022, vol. 14, issue 3, 10

Abstract: In this paper, the finite difference method is used to solve the positive fractional derivative damped string vibration equations, and the vibration attenuation phenomenon of the model is described by numerical simulation. In numerical examples, the effects of the order of the positive definite fractional derivative and the damping coefficient on vibration are studied and compared respectively. The results show that, on the one hand, when the damping coefficient c is fixed, the closer the order p(0 < p < 1) is to 1, the faster the attenuation is. On the other hand, when the order p is fixed, the larger the damping coefficient c is, the faster the attenuation is.

Date: 2022
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