高等数学中辅助函数的构造方法

辅助函数在高等数学中有着广泛的应用,总结了三种常见的构造辅助函数的技巧零值定理法、原函数法和常数值法。

浅析辅助函数的构造及应用

阐述了辅助函数的基本特征与构造辅助函数的原则,并介绍几种较为典型的构造辅助函数的方法应用.

Basic Numerical Computational Using Scilab Programming

Mathematics is very important for the engineering and scientist but to make understand the mathematics is very difficult if without proper tools and suitable measurement. A numerical method is one of the algorithms which involved with computer programming. In this paper, Scilab is used to carter the problems related the mathematical models such as Matrices, operation with ODE＇s and solving the Integration.

Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations

The aim of this paper is to obtain numerical solutions of the one-dimensional,two-dimensional and coupled Burgers' equations through the generalized differential quadrature method(GDQM).The polynomial-based differential quadrature(PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta(TVD-RK) method.The numerical solutions are satisfactorily coincident with the exact solutions.The method can compete against the methods applied in the literature.

Study on the Hydrolysis and Ammonolysis Kinetics of a Monochlorotriazinyl Reactive Dye

To understand the reaction behaviour of the reactive dye with amino groups on protein fibres,the reaction kinetics of competitive hydrolysis and ammonolysis of a monochlorotriazina reactive dye were studied at 50-80℃ and pH=8-10 by high performance liquid chromatography(HPLC).The results showed the pseudo-first-order phenomenon for the general reaction of concurrent hydrolysis and ammonolysis of the dyes.The ammonolysis reaction was always faster than the hydrolysis reaction in the range of temperature and pH employed,but the preference for ammonolysis to hydrolysis reaction decreased with the increase of temperature and pH value.The ratios of ammonolysis/hydrolysis rate constant reduced from 17.6 to 5.4 when the temperature increased from 50 to 80℃ in pH=10,and from 7.2 to 5.4 when the pH value increased from 8 to 10 at 80℃.

Elastic catenary cable element considering frictional slip effect

Conventional analysis methods of cable structures do not consider sliding of cables inside the joint,which may lead to inaccuracy of the theoretical behavior of the structure.In order to develop an effective method for cable sliding,a two-node cable element based on the analytical solution for an elastic catenary was studied.The cable sliding stiffness and the effect of friction were investigated.To validate the proposed numerical method,analyses of two examples given in the literature were conducted.The results demonstrated that the method given in this paper is accurate and effective,and can take into account cable sliding in cable structures.In addition,it was shown that the effect of cable sliding on the behavior of cable structures is significant.It was also shown that the friction at the support hampers the flow of the cable force,leading to unequal cable tensions on both sides of the support.

Simulation of Unsteady Flows with Fluctuating Inflow or Outflow Boundary Conditions

This paper describes the numerical simulation of unsteady flows due to incoming wakes and/or varying back pressure,The solution method is based upon the one-step finite-volume TVD Lax-Wendroff scheme.Dual time-step approach and multigrid algorithm are adopted to improve the computational efficiency of the baseline scheme.Numerical results for the transonic unsteady flow in a channel bump and the unsteady flow in a flat plate cascade and the VKI cascade are presented.

On the Numerical Solution to a Nonlinear Wave Equation Associated with the First Painlev Equation:an Operator-Splitting Approach

The main goal of this article is to discuss the numerical solution to a nonlinear wave equation associated with the first of the celebrated Painlevd transcendent ordinary differential equations. In order to solve numerically the above equation, whose solutions blow up in finite time, the authors advocate a numerical methodology based on the Strang＇s symmetrized operator-splitting scheme. With this approach, one can decouple nonlinearity and differential operators, leading to the alternate solution at every time step of the equation as follows： （i） The first Painlevd ordinary differential equation, （ii） a linear wave equation with a constant coefficient. Assuming that the space dimension is two, the authors consider a fully discrete variant of the above scheme, where the space-time discretization of the linear wave equation sub-steps is achieved via a Galerkin/finite element space approximation combined with a second order accurate centered time discretization scheme. To handle the nonlinear sub-steps, a second order accurate centered explicit time discretization scheme with adaptively variable time step is used, in order to follow accurately the fast dynamic of the solution before it blows up. The results of numerical experiments are presented for different coefficients and boundary conditions. They show that the above methodology is robust and describes fairly accurately the evolution of a rather ＂violent＂ phenomenon.

Unsteady 3D algebraically explicit analytical solutions for bio-heat transfer equations

Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is obtained in this paper.In other cases the temperature would vary monotonously along geometric coordinates as time goes by.There have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in literature.Besides its irreplaceable theoretical value,the analytical solution can also serve as standard solution to check numerical calculation,and therefore promote the development of numerical method of computational heat transfer.In addition,some new special methods have been given originally and deserved further attention.