### فهرست مطالب

• سال هشتم شماره 1 (Winter 2018)
• تاریخ انتشار: 1396/10/11
• تعداد عناوین: 6
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• Elham Afshari * Pages 1-14
In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in the Caputo sense. We propose a new finite difference method for solving time fractional diffu- sion equation. In our method firstly, we transform the Caputo derivative into Riemann-Liovill derivative. The stability and convergence of this method are investigated by a Fourier analysis. We show that this method is uncondition- ally stable and convergent with the convergence order O( 2+h2), where t and h are time and space steps respectively. Finally, a numerical example is given that confirms our theoretical analysis and the behavior of error is examined to verify the order of convergence.
Keywords: fractional derivative, finite difference method, stability, convergence, Fourier analysis, time fractional diffusion equation
• Vijaya Laxmi Pikkala *, Rajesh Pilla Pages 17-27
This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability \$b\$ or balk with \$bar{b} = 1-b\$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed to be exponentially distributed and are mutually independent. We have obtained the transient-state probabilities in terms of modified Bessel function of the first kind by employing probability generating function, continued fractions and Laplace transform. In addition, we have also obtained some other performance measures.
Keywords: queue, transient probabilities, variant working vacations, balking, probability generating function, continued fractions, Laplace transform
• Driss Sbibih *, Bachir Belkhatir Pages 29-38
In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters within a rational cubic Bézier curve should be determined by minimizing a maximum error. We finish by proving and justifying the efficiently of the approaching method with some comparative numerical and graphical examples.
Keywords: Hermite interpolation, Rational curve, G^2 continuity, Geometric conditions, Optimization