HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

Laguerre-Gauss collocation method for initial value problems of second order ODEs

This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency.

Structure and Performance of Fe-N_x-C Catalyst for Oxygen Reduction Reaction Prepared by Vacuum Casting Method and the Second Pyrolysis

Affordable non-precious metal（NPM） catalysts played a vital role in the wide application of polymer electrolyte membrane fuel cells（PEMFC）. In current work, a facile vacuum casting reacting method based on vacuum casting was introduced to prepare Fe-N_x-C oxygen reduction reaction（ORR） catalysts with high efficient in acid medium. The catalysts were prepared with ammonium ferrous sulfate hexahydrate（AFS） and 1,10-phenanthroline monohydrate utilizing homemade mesoporous silica template. The heat treatment and its influence on structure and performance were systematically evaluated to achieve superior ORR performance and some clues were found. And 850 ℃ was found to be the best temperature for the first and second pyrolysis. The linear sweep voltammetry（LSV） results showed that there were only 18 mV slightly negative shifts of half-wave potential（E_（1/2）） of the optimal catalyst（749 mV） compared with the commercial Pt/C（20 μg·Pt·cm^-2）. Besides, I850 R also showed better electrochemical stability and methanol-tolerance than that of Pt/C. All evidences proved that our vacuum casting reacting strategy and heat treatment process were prospective for the future R＆D of high performance Fe-N_x-C ORR catalysts.

Two-grid partition of unity method for second order elliptic problems

A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in HI-norm. Furthermore, it is shown that the L^2 error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results.

AN ADI GALERKIN METHOD WITH MOVING FINITE ELEMENT SPACES FOR A CLASS OF SECOND-ORDER HYPERBOLIC EQUATIONS

An alternating direction implicit (ADI) Galerkin method with moving finite element spaces is formulated for a class of second order hyperbolic equations in two space variables. A priori H 1 error estimate is derived.

A Semi-Analytical Method for Solutions of a Certain Class of Second Order Ordinary Differential Equations

This paper presents the theory and applications of a new computational technique referred to as Differential Transform Method (DTM) for solving second order linear ordinary differential equations, for both homogeneous and nonhomogeneous cases. For the robustness and efficiency of the method, four examples are considered. The results indicate that the DTM is reliable and accurate when compared to the exact solutions of the solved problems.

The Successive Approximation Method for Solving Nonlinear Fredholm Integral Equation of the Second Kind Using Maple

In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results appear that this method is very effective and convenient to solve these equations.

Explicit Iterative Methods of Second Order and Approximate Inverse Preconditioners for Solving Complex Computational Problems

Explicit Exact and Approximate Inverse Preconditioners for solving complex linear systems are introduced. A class of general iterative methods of second order is presented and the selection of iterative parameters is discussed. The second order iterative methods behave quite similar to first order methods and the development of efficient preconditioners for solving the original linear system is a decisive factor for making the second order iterative methods superior to the first order iterative methods. Adaptive preconditioned Conjugate Gradient methods using explicit approximate preconditioners for solving efficiently large sparse systems of algebraic equations are also presented. The generalized Approximate Inverse Matrix techniques can be efficiently used in conjunction with explicit iterative schemes leading to effective composite semi-direct solution methods for solving large linear systems of algebraic equations.

A Second Order Characteristic Mixed Finite Element Method for Convection Diffusion Reaction Equations

A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.

Differential Quadrature Method for Steady Flow of an Incompressible Second-Order Viscoelastic Fluid and Heat Transfer Model

The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a snmll parameter to get the zeroth- and first-order approximate equations. By using the differenl2al quadrature method with only a few grid points, the high-accurate numerical results were obtained.

Research on the Related Factors of the Second Molar Dislocation and Orthodontic Erect Method

The second molar dislocation is more common clinically.To investigate the related factors of the second permanent molar dislocation,and provide reference for the clinical diagnosis and treatment of orthodontics.From the current clinical research,the clinical methods of orthodontic erect secondary molars are also diverse and clinical.The narrower first molar alveolar arch width,smaller ANB angle,and crowded maxillary posterior segment arch are the factors that cause the maxillary second permanent molar dislocation.The narrow alveolar arch width,the smaller SNB angle,the larger ANB angle,and the crowded lower mandibular arch are the factors leading to the dislocation of the mandibular second permanent molar.In addition,for the second mandibular molar malposition,it is particularly important to select the corrective treatment plan.It is especially important to improve the treatment.

Application of diflerential constraint method to exact solution of second-grade fluid

A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.

Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure

The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspon- dence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale （SOTS） computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calcu- lating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement ap- proximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure.

P-and S-wavefield simulations using both the firstand second-order separated wave equations through a high-order staggered grid finite-difference method

In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations： the first-order （velocity-stress） and the second- order （displacement-stress） separate elastic wave equa- tions, with the first-order （velocity-stress） and the second- order （displacement-stress） full （or mixed） elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.

An Efficient Method for Reliability-based Multidisciplinary Design Optimization

Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization （MDO） techniques for the design of complex engineering system. An advanced first order second moment method-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and the reliability analysis methods. It is seen through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.

Second-line treatments for advanced gastric cancer: Interpreting outcomes by network meta-analysis

AIM: To study the effectiveness of second-linetreatments for advancer gastric cancer by application of Bayesian network meta-analysis.METHODS: Our search covered the literature up to February 2015. The following 6 treatments were evaluated:(1) irinotecan(camptothecins);(2) paclitaxel(taxanes class);(3) docetaxel(taxanes);(4) everolimus(mammalian target of rapamycin inhibitors);(5) ramucirumab(vascular endothelial growth factor receptor 2 inhibitors);(6) ramucirumab + paclitaxel. Our methodology was based on standard models of Bayesian network meta-analysis. The reference treatment was best supportive care(BSC). The endpoint was overall survival. Median survival was the outcome measure along with 95% credible intervals. RESULTS: Our search identified a total of 7 randomized controlled trials. These trials included 2298 patients(in 15 treatment arms) in whom a total of 6 active treatments were evaluated as well as BSC. There were 21 head-to-head comparisons(6 direct, 15 indirect). The difference in survival between each of two active treatments(paclitaxel and ramucirumab + paclitaxel) vs BSC was statistically significant, while the other 4 showed no statistical difference. In the 6 head-to-head comparisons between active treatments, no significant survival difference was demonstrated. CONCLUSION: Our results indicate that both paclitaxel monotherapy and ramucirumab + paclitaxel determine a significant prolongation in survival as compared with BSC.

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

Tungsten nanoparticle-strengthened copper composite prepared by a sol–gel method and in-situ reaction

Tungsten nanoparticle-strengthened Cu composites were prepared from nanopowder synthesized by a sol–gel method and in-situ hydrogen reduction.The tungsten particles in the Cu matrix were well-dispersed with an average size of approximately 100–200 nm.The addition of nanosized W particles remarkably improves the mechanical properties,while the electrical conductivity did not substantially decrease.The Cu–W composite with 6 wt%W has the most comprehensive properties with an ultimate strength of 310 MPa,yield strength of 238 MPa,hardness of HV 108 and electrical conductivity of 90%IACS.The enhanced mechanical property and only a small loss of electrical conductivity demonstrate the potential of this new strategy to prepare W nanoparticle-strengthened Cu composites.

Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.

An Improved Splitting Method

In this paper, an improved splitting method, based on the completely square-conservative explicit difference schemes, is established. Not only can the time-direction precision of this method be higher than that of the traditional splitting methods but also can the physical feature of mutual dependence of the fast and the slow stages that are calculated separately and splittingly be kept as well. Moreover, the method owns an universality, it can be generalized to other square-conservative difference schemes, such as the implicit and complete ones and the explicit and instantaneous ones. Good time benefits can be acquired when it is applied in the numerical simulations of the monthly mean currents of the South China Sea.