The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nyström (RKN) methods with varying step sizes is investigated. Perturbation methods are used to quantify the critical step sizes associated with parametric instability. It is shown that there is no parametric instability for linear constant coefficient ODEs integrated with ...

Abstract In this paper we examine the stability of stellar configurations in which interior solution is described by a closed Friedmann-Lemaître-Robertson-Walker (FLRW) geometry sourced with charged pressureless fluid and radiation. An interacting vacuum component conformally coupled massive scalar field are also included. Given simple factor for energy transfer between obtain bounded oscillato...

The dynamic characteristics and parametric instability of a rotating electrorheological ER sandwich beam with rotary oscillation are numerically analyzed. Assuming that the angular velocity of an ER sandwich beam varies harmonically, the dynamic equation of the rotating beam is first derived based on Hamilton’s principle. Then the coupling and nonlinear equation is discretized and solved by the...

In this article, vibration characteristics and the parametric instability of functionally graded material (FGM) plates with cyclic loading in a hygrothermal field are discussed. The plate element is modeled in a finite element by applying the third-order shear deformation hypothesis. The mathematical formulation of the FGM plate is made with two material constituents by applying the power rule ...

  Propagation of dust ion acoustic waves in plasmas composed of nonthermal distributed electrons and stationary dust particles is investigated. Nonlinear Schrdinger equation is derived to describe small amplitude waves, using the reduction perturbation technique. Modulation instability of dust ion acoustic waves is analysed for this system. Parametric investigation indicates that growth rate of...