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This paper is concerned with two alternating direction implicit (ADI) finite difference methods for solving a two-dimensional fractional subdiffusion equation. An explicit error estimate for each of the two methods is provided in the discrete maximum norm. It is shown that the methods have the same order as their truncation errors with respect to the discrete maximum norm. Numerical results are given to confirm the theoretical analysis results.

ZigBee is an emerging standard specifically designed for wireless personal area networks (WPANs) with a focus on enabling the wireless sensor networks (WSNs). It attempts to provide a low-data rate, low-power, and low-cost wireless networking on the device-level communication. In this paper, we have established a realistic indoor environment for the performance evaluation of a 51-node ZigBee wireless network. Several sets of practical experiments have been conducted to study its various features, including the (1) node connectivity, (2) packet loss rate, and (3) transmission throughput. The results show that our developed ZigBee platforms could work well under multihop transmission over an extended period of time.

We propose a new compact alternating direction implicit (ADI) finite difference scheme on uniform meshes for a weakly singular integro-differential equation in three space dimensions. Compared with the compact non-ADI scheme, the proposed compact ADI scheme is easy to implement and significantly reduces the computational cost of solving the resulting linear system, while maintaining the same order of the local truncation error. We prove that the new compact ADI scheme is unconditionally stable, and has second-order convergence in time and fourth-order convergence in space for weakly singular solutions. Numerical results are given to confirm the theoretical analysis result and demonstrate the computational efficiency of the proposed compact ADI scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with numerical methods for a class of two-dimensional quasilinear elliptic boundary value problems. A compact finite difference method with a nonisotropic mesh is proposed for the problems. The existence of a maximal and a minimal compact difference solution is proved by the method of upper and lower solutions, and two sufficient conditions for the uniqueness of the solution are also given. The optimal error estimate in the discrete L∞ norm is obtained under certain conditions. The error estimate shows the fourth-order accuracy of the proposed method when two spatial mesh sizes are proportional. By using an upper solution or a lower solution as the initial iteration, an galmost optimalh Picard type of monotone iterative algorithm is presented for solving the resulting nonlinear discrete system efficiently. Applications using two model problems give numerical results that confirm our theoretical analysis. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to give a numerical treatment for a class of nonlinear multipoint boundary value problems. The multipoint boundary condition under consideration includes various commonly discussed boundary conditions, such as the three- or four-point boundary condition. The problems are discretized by the fourth-order Numerov's method. The existence and uniqueness of the numerical solution are investigated by the method of upper and lower solutions. The convergence and the fourth-order accuracy of the method are proved. An accelerated monotone iterative algorithm with the quadratic rate of convergence is developed for solving the resulting nonlinear discrete problems. Some applications and numerical results are given to demonstrate the high efficiency of the approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite difference solutions of a system of reaction-diffusion equations with coupled nonlinear boundary conditions and time delays. The reaction functions and the boundary functions are not necessarily quasimonotone, and the time delays may appear in the reaction functions as well as in the boundary functions. The investigation is devoted to the finite difference system for both the time-dependent problem and its corresponding steady-state problem. Some monotone iteration processes for the finite difference systems are given, and the asymptotic behavior of the time-dependent solution in relation to the steady-state solution is discussed. The asymptotic behavior result leads to some local and global attractors of the time-dependent problem, including the convergence of the time-dependent solution to a unique steady-state solution. An application and some numerical results to an enzyme-substrate reaction-diffusion problem are given. All the results are directly applicable to parabolic-ordinary systems and to reaction-diffusion systems without time delays. [ABSTRACT FROM AUTHOR]

In order to accurately predict the single event upsets (SEU) rate of on-orbit proton, the influence of the proton energy distribution, incident angle, supply voltage, and test pattern on the height, width, and position of SEU peak of low energy protons (LEP) in 65 nm static random access memory (SRAM) are quantitatively evaluated and analyzed based on LEP testing data and Monte Carlo simulation. The results show that different initial proton energies used to degrade the beam energy will bring about the difference in the energy distribution of average proton energy at the surface and sensitive region of the device under test (DUT), which further leads to significant differences including the height of SEU peak and the threshold energy of SEU. Using the lowest initial proton energy is extremely important for SEU testing with low energy protons. The proton energy corresponding to the SEU peak shifts to higher average proton energies with the increase of the tilt angle, and the SEU peaks also increase significantly. The reduction of supply voltage lowers the critical charge of SEU, leading to the increase of LEP SEU cross section. For standard 6-transitor SRAM with bit-interleaving technology, SEU peak does not show clear dependence on three test patterns of logical checkerboard 55H, all “1”, and all “0”. It should be noted that all the SEUs in 65 nm SRAM are single cell upset in LEP testing due to proton’s low linear energy transfer (LET) value. [ABSTRACT FROM AUTHOR]