Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A...

Two discrete-time orthogonal spline collocation schemes are formulated and analyzed for solving the linear time-dependent Schrr odinger equation in two space variables. These are Crank-Nicolson and alternating direction implicit (ADI) schemes employing C 1 piecewise polynomial spaces of arbitrary degree 3 in each space variable. The stability of the schemes is examined and optimal order a prior...

This paper presents an improved gas-kinetic scheme based on the Bhatnagar– Gross–Krook (BGK) model for the compressible Navier–Stokes equations. The current method extends the previous gas-kinetic Navier–Stokes solver developed by Xu and Prendergast (J. Comput. Phys. 114, 9) by (a) implementing a general nonequilibrium state based on the Chapman–Enskog expansion of the BGK model as the initial ...

This work analyzes the asymptotic performances of fully distributed sequential hypothesis testing procedures as the type-I and type-II error rates approach zero, in the context of a sensor network without a fusion center. In particular, the sensor network is defined by an undirected graph, where each sensor can observe samples over time, access the information from the adjacent sensors, and per...

We prove that the two-step backward differentiation formula (BDF) method is stable on arbitrary time grids; while variable-step three-step scheme if almost all adjacent step ratios are less than 2.553. These results relax severe mesh restrictions in literature and provide a new understanding of BDF methods. Our main tools include discrete orthogonal convolution kernels an elliptic type matrix n...

In the current work we construct a nonlocal mathematical model describing the phase transition occurs during the resistance spot welding process in the industry of metallurgy. We then consider a time discretization scheme for solving the resulting nonlocal moving boundary problem. The scheme consists of solving at each time step a linear elliptic partial differential equation and then making a ...

Abstract. This paper presents a new algorithm for the numerical solution of the Navier-Stokes equations coupled with the convection-diffusion equation. After establishing convergence of the semi-discrete formulation at each time step, we introduce a new iterative scheme based on a projection method called Coupled Prediction Scheme (CPS). We show that even though the predicted temperature is adv...

In this paper, using the locally optimum (LO) test statistic, a joint decision rule of two correct cells is derived for nonselective Rayleigh fading channels. Then, we propose a new acquisition scheme based on the joint decision rule. The mean acquisition time performance of the proposed acquisition scheme is analyzed and compared with that of a conventional acquisition scheme in which only one...