Numerical Solution of the Distributed-Order Fractional Bagley-Torvik Equation

In this paper, two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation.This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect to the nonnegative density function. Using the composite Boole's rule the distributedorder Bagley-Torvik equation is approximated by a multi-term time-fractional equation, which is then solved by the GrunwaldLetnikov method(GLM) and the fractional differential transform method(FDTM). Finally, we compared our results with the exact results of some cases and show the excellent agreement between the approximate result and the exact solution.

Intermittent Control for Fixed-Time Synchronization of Coupled Networks

Dear Editor, This letter deals with fixed-time synchronization(Fd-TS) of complex networks(CNs) under aperiodically intermittent control(AIC)for the first time. The average control rate and a new Lyapunov function are proposed to overcome the difficulty of dealing with fixedtime stability/synchronization of CNs for AIC.

The Multi-scale Method for Solving Nonlinear Time Space Fractional Partial Differential Equations

In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.

Adaptive Algorithm for Accelerating Direct Isosurface Rendering on GPU

Direct isosurface volume rendering is the most prominent modern method for medical data visualization.It is based on finding intersection points between the rays corresponding to pixels on the screen and isosurface. This article describes a two-pass algorithm for accelerating the method on the graphic processing unit(GPU). On the first pass, the intersections with the isosurface are found only for a small number of rays, which is done by rendering into a lower-resolution texture. On the second pass, the obtained information is used to efficiently calculate the intersection points of all the other. The number of rays to use during the first pass is determined by using an adaptive algorithm, which runs on the central processing unit(CPU) in parallel with the second pass of the rendering. The proposed approach allows to significantly speed up isosurface visualization without quality loss. Experiments show acceleration up to 10 times in comparison with a common ray casting method implemented on GPU. To the authors’ knowledge, this is the fastest approach for ray casting which does not require any preprocessing and could be run on common GPUs.