复域内一般微分方程组的非允许解

在文［８］中,我们已给出了复域内微分方程组的ｍ分量－允许解之定义,在本文里,我们类似给出复域内微分方程组的ｍ分量－非允许解之定义并讨论了更广泛的复域内微分方程组的这种解的存在性,得到了一些结果。     

复微分方程组的m分量-可允许解

本文给出了复域内一类代数微分方程组的ｍ分量－可允许解之定义，并利用Ｎｅｖａｎｌｉｎｎａ值分布理论讨论了这类微分方程组的这种解的存在性，得到了更精确、更一般的结果．     

一类微分方程组的非允许解

利用亚纯函数Nevanlinna的值分布理论，我们研究了一类代数微分方程组非允许解的存在性问题。并通过亏量δ(a，w)改进了非允许解的估计．     

一类高阶非线性微分方程组的亚纯允许解

利用亚纯函数的Nevanlinna值分布理论和微分方程的研究技巧,研究一类高阶非线性微分方程组的亚纯解,并且微分方程组的亚纯解或同为允许的,或同为非允许的.推广和改进了一些结论.     

一类高阶非线性代数微分方程组的亚纯允许解

利用亚纯函数的Nevanlinna值分布理论,研究一类高阶非线性代数微分方程组的亚纯解的存在性问题,获得微分方程组的亚纯解或同为允许的,或同为非允许的,进而得到更一般的结果.     

Cn 中一类复高阶偏微分方程组的允许解

本文研究了多复变中一类复高阶偏微分方程组的允许解的存在性问题,利用多复变值分布理论和技巧,获得一类复高阶偏微分方程组在给定条件下,其允许解的性质.并将单复微分方程组中的一些结果推广到多复变中.     

复微分方程组允许解的一个结果

本文利用亏量对复微分方程组的允许解的估计进行了改进，得到了一个主要结果。     

具有允许解的代数微分方程组的形式

本文以不同于以往研究复微分方程组的方法,讨论了一类具有允许解的代数微分方程组的形式,得到了一个主要结果。     

一类微分方程组的非齐次Sturm-Liouville边值问题解的存在性

在允许非线性项变号的情况下,利用锥上不动点定理,讨论了一类二阶非线性微分方程组的非齐次Sturm-Liouville边值问题解的存在性,得到了至少一个解及正解存在的多个存在性定理．     

线性非齐次微分方程（组）的算值解法

线性非齐次微分方程（组）的算值解法于桂珍（天津大学）根据线性非齐次微分方程（组）解的结构定理，线性非齐次微分方程（组）的通解等于对应的齐次方程（组）的通解加上非齐次方程（组）的一个特解。对于常系数线性方程（组）来说，当非齐次项为某些特殊形式时，可用待...     

On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations

This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda＇s results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations.     

Approximations of the nonlinear Volterra's population model by an efficient numerical method

In this paper, we apply the new homotopy perturbation method to solve the Volterra's model for population growth of a species in a closed system. This technique is extended to give solution for nonlinear integro‐differential equation in which the integral term represents the total metabolism accumulated fromtime zero. The approximate analytical procedure only depends on two components. The newhomotopy perturbationmethodwas applied to nonlinear integro‐differential equations directly and by converting the problem into nonlinear ordinary differential equation. We also compare this method with some other numerical results and show that the present approach is less computational and is applicable for solving nonlinear integro‐differential equations and ordinary differential equations as well. Copyright © 2011 John Wiley & Sons, Ltd.     

Solving systems of fractional differential equations using differential transform method

This paper presents approximate analytical solutions for systems of fractional differential equations using the differential transform method. The fractional derivatives are described in the Caputo sense. The application of differential transform method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations, using symbolic computation. The numerical results show that the approach is easy to implement and accurate when applied to systems of fractional differential equations. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations.     

Numerical approach to differential equations of fractional order

In this paper, the variational iteration method and the Adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. This paper presents a numerical comparison between the two methods for solving systems of fractional differential equations. Numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order.     

A novel variational method for 3D viscous flow in flow channel of turbomachines based on differential geometry

ABSTRACT

This paper presents a novel variational method for treating three-dimensional rotational Navier-Stokes equations in flow channel of turbomachines. The proposed method establishes a new semi-geodesic coordinate system on the central surface of blades. From the perspective of differential geometry, the system under concern is split into a set of membrane operator equations on two-dimensional manifolds and bending operator equations along hub circle. The third variable of the new coordinate system is approximated by the central difference scheme. We derive a new formulation of two-dimensional Navier-Stokes equations with three components on the manifolds in the variational sense. The well-posedness of the proposed variational formulation is rigorously justified.     

Equations of anisotropic elastodynamics in 3D quasicrystals as a symmetric hyperbolic system: Deriving the time-dependent fundamental solutions

The fundamental solution (FS) of the time-dependent differential equations of anisotropic elasticity in 3D quasicrystals are studied in the paper. Equations of the time-dependent differential equations of anisotropic elasticity in 3D quasicrystals are written in the form of a symmetric hyperbolic system of the first order. Using the Fourier transform with respect to the space variables and matrix transformations we obtain explicit formulae for Fourier images of the FS columns; finally, the FS is computed by the inverse Fourier transform. As a computational example applying the suggested approach FS components are computed for icosahedral QCs.     

On the solution of the Abel equation of the second kind by the shifted Chebyshev polynomials

This paper presents a new approximate method of Abel differential equation. By using the shifted Chebyshev expansion of the unknown function, Abel differential equation is approximately transformed to a system of nonlinear equations for the unknown coefficients. A desired solution can be determined by solving the resulting nonlinear system. This method gives a simple and closed form of approximate solution of Abel differential equation. The solution is calculated in the form of a series with easily computable components. The numerical results show the effectiveness of the method for this type of equation. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate.     

Properties of solutions of stochastic differential equations with continuous-state-dependent switching

This work is concerned with several properties of solutions of stochastic differential equations arising from hybrid switching diffusions. The word “hybrid” highlights the coexistence of continuous dynamics and discrete events. The underlying process has two components. One component describes the continuous dynamics, whereas the other is a switching process representing discrete events. One of the main features is the switching component depending on the continuous dynamics. In this paper, weak continuity is proved first. Then continuous and smooth dependence on initial data are demonstrated. In addition, it is shown that certain functions of the solutions verify a system of Kolmogorov's backward differential equations. Moreover, rates of convergence of numerical approximation algorithms are dealt with.     

Higher order fully discrete scheme combined withH 1-Galerkin mixed finite element method for semilinear reaction-diffusion equations

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by anH ¹-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) ofindex one. Apriori error estimates for semidiscrete scheme are derived for both differential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.     

Charpit System of Partial Differential Equations with Algebraic Constraints

In this paper the Charpit system of partial differential equations with algebraic constraints is considered. So, first the compatibility conditions of a system of algebraic equations and also of the Charpit system of partial differential equations are separately considered. For the combined system of equations of both types sufficient conditions for the existence of a solution are found. They lead to an algorithm for reducing the combined system to a Charpit system of partial differential equations of dimension less than the initial system and without algebraic constraints. Moreover, it is proved that this system identically satisfies the compatibility conditions if so does the initial system.