in this paper, controlling the gyros with linear plus cubic damping is considered. hence, an adaptive control algorithm is proposed to overcome the uncertainties in model parameters and the chaotic behavior of gyroscopes. it is noted that for general applications dynamic model coefficient of gyros is not precisely determined, on the other hand, with respect to a particular coefficient gyroscope...

we are concerned with the development of a k−step method for the numerical solution of fuzzy initial value problems. convergence and stability of the method are also proved in detail. moreover, a specific method of order 4 is found. the numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

In this paper, we present variable-stepsize explicit parallel peer methods grounded in the interpolation idea. Approximation, stability, and convergence are studied in detail. In particular, we prove that some interpolating peer methods are stable on any variable mesh in practice. Double quasi consistency is utilized to introduce an efficient global error estimation formula in the numerical met...

In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...

We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1 < α ≤ 2. This operator is defined by a combination of the left and right Riemann–Liouville fractional derivatives. We stu...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...