非线性双曲型积分微分方程有限元逼近的误差分析

考虑非线性双曲型积分微分方程半离散有限格式 ,得到H1超收敛和最优阶L∞ 和Wl,∞ 模误差估计 .

关于Volterra积分微分方程稳定性的分解问题

一、前言 本文研究具有分解

The Robin Problem for Singular Perturbed Integral Differential Equations of Volterra Type

In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,under the appropriate assumptions,by constructing the special function of upper and lower solutions,we demonstrate the existence of the solution for singularly preturbed integral differential equation of Volterra type,and give the uniformly valid approximate estimation.

A new method for integration of a Birkhoffian system

The idea of the gradient method for integrating the dynamical equations of a nonconservative system presented by Vujanovic is transplanted to a Birkhoffian system, which is a new method for the integration of Birkhoff＇s equations. First, the differential equations of motion of the Birkhoffian system are written out. Secondly, 2n Birkhoff＇s variables are divided into two parts, and assume that a part of the variables is the functions of the remaining part of the variables and time. Thereby, the basic quasi-linear partial differential equations are established. If a complete solution of the basic partial differential equations is sought out, the solution of the problem is given by a set of algebraic equations. Since one can choose n arbitrary Birkhoff＇s variables as the functions of n remains of variables and time in a specific problem, the method has flexibility. The major difficulty of this method lies in finding a complete solution of the basic partial differential equation. Once one finds the complete solution, the motion of the systems can be obtained without doing further integration. Finally, two examples are given to illustrate the application of the results.

Mathematical model for precursor gas residence time in isothermal CVD process of C/C composites

In the chemical vapor deposition（CVD） process of C/C composites,the dynamics and mechanism of precursor gas flowing behavior were analyzed mathematically,in which the precursor gas was infiltrated by the pressure difference of the gas flowing through felt.Differential equations were educed which characterized the relations among the pressure inside the felt,the pressure outside the felt of the precursor gas and the porosity of the felt as a function of CVD duration.The gas residence time during the infiltration process through the felt was obtained from the differential equations.The numerical verification is in good agreement with the practical process,indicating the good reliability of the current mathematical model.

Parametric analysis of mixed lubrication characteristics in work zone of strip rolling

A theoretical model for mixed lubrication with more accurate contact length has been developed based on the average volume flow model and asperity flattening model,and the lubricant volume flow rate and outlet speed ratio are determined by integrating differential equations based on rolling parameters.The lubrication characteristics at the roll-strip interface with different surface roughness,rolling speed,reduction and lubricant viscosity are analyzed respectively.Additionally,the average volume flow rates of lubricant under different rolling conditions are calculated and used to explain the change rule of lubrication characteristics.The developed scheme is able to determine the total pressure,lubricant pressure,film thickness and real contact area at any point within the work zone.The prediction and analysis of mixed lubrication characteristics at the interface is meaningful to better control the surface quality and optimize the rolling process.

The Most Probable Mechanism Function and Kinetic Parameters of Gibbsite Dissolution in NaOH

Determination of probable mechanism function and kinetic parameters is important to hydrometallurgical kinetics.In this work,the most probable mechanism function and kinetic parameters of gibbsite dissolution in NaOH solution are studied.The sample,the mixture of synthetic gibbsite and sodium hydroxide solution,was scanned in high-pressure differential scanning calorimetry(DSC) equipment with the heating rate of 10 K·min-1. Integral equation and differential equation of non-isothermal kinetics were solved to fit the data related to DSC curve.According to the calculation results,the most probable mechanism function for pure synthetic gibbsite dissolution in sodium hydroxide solution is presented based on the optimum procedure in the database of the mechanism function.The apparent activation energy obtained is(75±1) kJ·mol-1,the frequency factor is 10 8±1mol·s-1,and the reaction is a second order reaction.

The Integrable Conditions of Riccati Differential Equation

In this paper,the new integrable conditions of Riccati equation is presented by invarant of Riccati equation.

A New (2+1)-Dimensional Integrable Equation

A new nonlinear partial differential equation （PDE） in 2＋1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal resealing. In order to demonstrate integrability property of the new equation, the corresponding Lax pair is obtained by applying the reduction technique to the Lax pair of the mKP equation.

The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

Trotter-kato Theorems for an α-times Integrated Semigroups

In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.

Application of Fractional Calculus to a Linear Third Order (Nonhomogeneous and Homogeneous) Ordinary Differential Equation

In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f.

Energy-Work Connection Integration Scheme for Nonholonomic Hamiltonian Systems

This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration schemes are presented. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multi-stage schemes of order 2, its order of accuracy is 2n. The connection, which is discrete analogue of usual case, between the change of energy and work of nonholonomic constraint forces is obtained for nonholonomie Hamiltonian systems. This paper also gives that there is smaller error of the scheme when taking a large number of stages than a less one. Finally, an applied example is discussed to illustrate these results.

The First Integral Method to Study a Class of Reaction-Diffusion Equations

In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.

A Finite Volume Backward Euler Difference Method for Nonlinear Parabolic Integral-differential Equation

The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations.These results are new for finite volume element methods for parabolic integro-differential equations.

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.

Initial Value Problems for Second Order Impulsive Integro-Differential Equation in Banach Spaces

By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differential equation in Banach spaces is obtained and the related results are essentially improved.At the same time, another sufficient condition of existence of minimal and maximal solutions based on the Kuratowski measure of noncompactness is given.

Globally Asymptotic Stability of Equilibrium of a Dynamical Model with Infinite Delay

By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in the reference [ 10] got by the second author herself.

Existence of Positive Solution to a Singular System of Nonlinear Fractional Differential Equation

In this paper,we discuss a singular system of nonlinear fractional differential equation,in which the inhomogeneous term depends on the fractional derivative of lower order.By using the Krasnoselskii＇s fixed point theorem and the Leray-Schauder nonlinear alternative method,some suffcient conditions for the existence of positive solution of the singular system are obtained.

Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations(ODEs),which may be gotten by a simple but unfamiliar Lax pair.Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies.The key is a special form of Lax pair for the AKNS hierarchy.It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.