.... This family of problems covers several linear fractional difference equations that appear in the literature. Numerical examples are given to justify our theory. 1 Corresponding author. 18 11 2022 04 04 2023 21 04 2023 forward operator discrete fractional non-autonomous...

... algorithms. In general, the proposed method is shown to be second-order accurate and unconditionally stable for linear elastic and stiffness softening systems. The comprehensive stability and accuracy analysis, including numerical dispersion, energy dissipation, and the overshoot behavior, are carried out...

... equation, we verify that the solution of such model may not be globally well-defined, and the dynamics of this model depends on the order of fractional derivative and the volume of spatial domain. In simulation, a finite difference scheme is implemented and interesting numerical solutions of model...

...M. A. Zaky; E. H. Doha; J. A. Tenreiro Machado In this paper, we construct and analyze a Legendre spectral-collocation method for the numerical solution of distributed-order fractional initial value problems. We first introduce three-term recurrence relations for the fractional integrals...

... 25.6907 RK3 low storage 1.33 26.104 HRK31 1.33 26.1174 HRK42 2.83 26.5724 RK4 classical 1.17 29.1903 HRK41 2.19 26.4474 Numerical dissipation ( ϵ D ) is a function of Δ x , CFL, Δ t and discretization used. All the values tabulated in Table 2...

... Multibody system dynamics Nonlinear dynamical systems Design optimization Robotics Impact Contact Friction modeling Numerical Integration methods Bio-mechanical systems Biological systems Dynamics Stability of nonlinear systems Design sensitivity Nonlinear systems Mechanism systems...

... fictitious damping is applied. Conventional DR methods use a fictitious mass matrix to increase the fictitious damping while maintaining numerical stability. There are many calculation methods for the fictitious mass matrix; however, it is difficult to select the appropriate method. In addition...

... 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- β algorithm. Numerical results show that the presented method has second-order accuracy...

.... Numerical examples confirm the superior accuracy of the proposed method. D efinition 1. The Riemann–Liouville fractional integration of order ν ≥ 0 is defined as ( I ν f ) ( t ) = { 1 Γ ( ν ) ∫ 0 t ( t − τ ) ν − 1 f ( τ ) d τ...

... a relatively large time integral step with numerical stability in computations. By simplifying into a linearized model, pseudo-excitation method (PEM) can be theoretically implemented to characterize the dominant vibration frequencies of vehicle-track systems due to random excitations. Finally, a trail method...

...; published online May 30, 2018. Assoc. Editor: Bogdan I. Epureanu. 03 10 2017 02 05 2018 Algorithms Experimental dynamics Numerical Integration methods Constructing a dynamic model from the observed data can be quite difficult for many complex engineered systems. This process...

.... , and Cortial , J. , 2014 , “ Dimensional Reduction of Nonlinear Finite Element Dynamic Models With Finite Rotations and Energy-Based Mesh Sampling and Weighting for Computational Efficiency ,” Int. J. Numer. Methods Eng. , 98 ( 9 ), pp. 625 – 662 . 10.1002/nme.4668 [3] Chaturantabut , S...

... as independent unknown parameters to be identified. Numerical simulations are conducted to identify two typical incommensurate fractional-order chaotic systems. Simulation results and comparisons analyses demonstrate that the proposed method is suitable for parameter identification with advantages of high...

... of view, the stability analysis and chaotic behavior of three novel fractional systems are provided by the proposed approach. Numerical simulations and comparative results confirm that this scheme is also successful for the fractional chaotic systems with delay arguments. 1 Corresponding author...

...-node beam element was introduced with a single translational degree-of-freedom. The stiffness matrix of this kind of element can be expressed by a single stiffness parameter. By connecting a few of these elements, a low degree-of-freedom model of rotors was created, which avoids some numerical...

... and applied to three typical quasi-periodic systems. The approximate boundaries in stability charts obtained from the proposed method are very close to the exact boundaries of original quasi-periodic equations computed numerically using maximal Lyapunov exponents. Further, the frequency spectra of solutions...

... level, is further modified via a “relaxation term” to morph what would otherwise be a nonlinear complementarity problem into a cone complementarity problem. The latter has a solution that is produced by solving of a convex quadratic optimization problem with conic constraints. The same numerical method...

...A. M. Nagy; N. H. Sweilam; Adel A. El-Sayed The multiterm fractional variable-order differential equation has a massive application in physics and engineering problems. Therefore, a numerical method is presented to solve a class of variable order fractional differential equations (FDEs) based...

...Samer S. Ezz-Eldien; Ahmed A. El-Kalaawy This paper presents an efficient approximation schemes for the numerical solution of a fractional variational problem (FVP) and fractional optimal control problem (FOCP). As basis function for the trial solution, we employ the shifted Jacobi orthonormal...

..., with a boundary condition in the infinite that describes the unsteady isothermal flow of a gas through a semi-infinite micro–nano porous medium and has widely used in the chemical industries. In this paper, a hybrid numerical method is introduced for solving this equation. First, by using the method of quasi...