Successively iterative method for fractional differential equations with integral boundary conditions

In this paper, we study the boundary value problem of a fractional differential equation with nonlocal integral boundary conditions. Two successively iterative sequences are constructed, the conditions for the existence of the nontrivial sign-changing solutions to the differential equation are established.     

A quasilinear singular elliptic system without cooperative structure

In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms.     

Comparisons of Stokes/Oseen/Newton iteration methods for Navier–Stokes equations with friction boundary conditions

In this paper, we make the comparison of Stokes/Oseen/Newton finite element iteration methods for solving the numerical solutions to Navier–Stokes equations with friction boundary conditions which are of the weak form of the variational inequality problem of the second kind. The comparison of these methods is reflected by the finite element error estimates in the energy norm for velocity and L²$L^2$ norm for pressure.     

集值渐近拟非扩张映射的不动点收敛定理

研究一致凸Banach空间中集值渐近拟非扩张映射的关于有限步迭代序列逼近公共不动点的充分必要条件,并在此条件下,证明了该序列收敛到公共不动点的一些强收敛定理,所得结果是单值映射情形的推广和发展.     

Iterative minimization of the Rayleigh quotient by block steepest descent iterations

The topic of this paper is the convergence analysis of subspace gradient iterations for the simultaneous computation of a few of the smallest eigenvalues plus eigenvectors of a symmetric and positive definite matrix pair (A,M). The methods are based on subspace iterations for A ^{? 1}M and use the Rayleigh‐Ritz procedure for convergence acceleration. New sharp convergence estimates are proved by generalizing estimates, which have been presented for vectorial steepest descent iterations (see SIAM J. Matrix Anal. Appl., 32(2):443‐456, 2011). Copyright © 2013 John Wiley & Sons, Ltd.     

Lie symmetry group analysis of magnetic field effects on free convective flow of a nanofluid over a semi-infinite stretching sheet

We investigate the steady two-dimensional flow of an incompressible water based nanofluid over a linearly semi-infinite stretching sheet in the presence of magnetic field numerically. The basic boundary layer equations for momentum and heat transfer are non-linear partial differential equations. Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations for this investigation are solved numerically using Nachtsheim–Swigert shooting iteration technique together with fourth order Runge–Kutta integration scheme. Effects of the nanoparticle volume fraction ϕ, magnetic parameter M, Prandtl number Pr on the velocity and the temperature profiles are presented graphically and examined for different metallic and non-metallic nanoparticles. The skin friction coefficient and the local Nusselt number are also discussed for different nanoparticles.     

A comparative study of numerical methods for solving the generalized Ito system

This paper is devoted to the numerical comparison of methods applied to solve the generalized Ito system. Four numerical methods are compared, namely, the Laplace decomposition method (LDM), the variation iteration method (VIM), the homotopy perturbation method (HPM) and the Laplace decomposition method with the Pade approximant (LD–PA) with the exact solution.     

Simulation studies of multi-line line-of-sight tunable-diode-laser absorption spectroscopy performance in measuring temperature probability distribution function

Line-of-sight tunable-diode-laser absorption spectroscopy（LOS-TDLAS） with multiple absorption lines is introduced for non-uniform temperature measurement. Temperature binning method combined with Gauss–Seidel iteration method is used to measure temperature probability distribution function（PDF） along the line-of-sight（LOS）. Through 100 simulated measurements, the variation of measurement accuracy is investigated with the number of absorption lines, the number of temperature bins and the magnitude of temperature non-uniformity. A field model with 2-T temperature distribution and15 well-selected absorption lines are used for the simulation study. The Gauss–Seidel iteration method is discussed for its reliability. The investigation result about the variation of measurement accuracy with the number of temperature bins is different from the previous research results.     

A QUASILINEAR SINGULAR ELLIPTIC SYSTEM WITHOUT COOPERATIVE STRUCTURE

In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms.     

Inner iterations in the shift-invert residual Arnoldi method and the Jacobi-Davidson method

We establish a general convergence theory of the Shift-Invert Residual Arnoldi(SIRA)method for computing a simple eigenvalue nearest to a given targetσand the associated eigenvector.In SIRA,a subspace expansion vector at each step is obtained by solving a certain inner linear system.We prove that the inexact SIRA method mimics the exact SIRA well,i.e.,the former uses almost the same outer iterations to achieve the convergence as the latter does if all the inner linear systems are iteratively solved with low or modest accuracy during outer iterations.Based on the theory,we design practical stopping criteria for inner solves.Our analysis is on one step expansion of subspace and the approach applies to the Jacobi-Davidson(JD)method with the fixed targetσas well,and a similar general convergence theory is obtained for it.Numerical experiments confirm our theory and demonstrate that the inexact SIRA and JD are similarly effective and are considerably superior to the inexact SIA.