in this paper, the dynamical behavior of an axially moving string modeled by fractional derivative is investigated. the governing equation represented motion is solved by the method of multiple scales. considering principal parametric resonance, the stability boundaries for string with simple supports are obtained. numerical results indicate the effects of fractional damping on stability.

The influence of physical damping on the numerical stability of time integration analysis is an open question since decades ago. In this paper, it is shown that, under specific very general conditions, physical damping can be disregarded when studying the numerical stability. It is also shown that, provided the specific conditions are met, analysis of structural systems involved in extremely hi...

In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...

Efficiency of numerical methods is an important problem in dynamic nonlinear analyses. It is possible to use of numerical methods such as beta-Newmark in order to investigate the structural response behavior of the dynamic systems under random sea wave loads but because of necessity to analysis the offshore systems for extensive time to fatigue study it is important to use of simple stable meth...

The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...

One problem which plagues the numerical evaluation of one-loop Feynman diagrams using recursive integration by part relations is a numerical instability near exceptional momentum configurations. In this contribution we will discuss a generic solution to this problem. As an example we consider the case of forward light-by-light scattering.

We consider a wave equation with fractional-order dissipative terms modeling viscothermal losses on the lateral walls of a duct, namely theWebster–Lokshin model. Diffusive representations of fractional derivatives are used, first to prove existence and uniqueness results, then to design a numerical scheme which avoids the storage of the entire history of past data. Two schemes are proposed depe...

ture formulae on bounded convex regions in the plane. The construction is based on the behavior of spectra of certain multiplication operators and leads to nodes which are inside a prescribed convex region in R. The resulting interpolation schemes are numerically stable and the quadrature formulae have positive weights and almost (but not quite) optimal numbers of nodes. The performance of the ...

Discretized representations of deformable objects, based upon simple dynamic point-mass systems, rely upon the propagation of forces between neighbouring elements to produce a global change in the shape of the surface. Attempting to make such a surface rigid produces stii equations that are costly to evaluate with any numerical stability. This paper introduces a new multilevel approach for cont...

In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to...