In this paper, we establish first a vector integro-differential inequality. Then by using the intequlity and the variation of constants formula to obtain some sufficient algebraic criteria for the stability and period...In this paper, we establish first a vector integro-differential inequality. Then by using the intequlity and the variation of constants formula to obtain some sufficient algebraic criteria for the stability and periodic solutions of a class of Volterra integro-differential largo-scale systems. Finally, some simple examples of application are given.展开更多
In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transforma...In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.展开更多
研究了一类新的非线性时滞Volterra-Fredholm型积分不等式.该不等式把文献[Ma,QH,Pecaric,J:Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities.Nonlinear Anal.69(2008)393-407]...研究了一类新的非线性时滞Volterra-Fredholm型积分不等式.该不等式把文献[Ma,QH,Pecaric,J:Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities.Nonlinear Anal.69(2008)393-407]中的函数σ_1(s)推广成函数w(u(s))f(s),其中w(u(s))是未知函数与非线性函数的复合函数.利用变量替换、放大及常量与变量的辩证关系等方法给出了该不等式中未知函数的估计.最后,用所得结果给出了一类积分方程解的估计.展开更多
This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems ...This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.展开更多
In this article, we study the Volterra integral equations with two kinds of delay that are proportional delay and nonproportional delay. We mainly use Chebyshev spectral collocation method to analyze them. First, we u...In this article, we study the Volterra integral equations with two kinds of delay that are proportional delay and nonproportional delay. We mainly use Chebyshev spectral collocation method to analyze them. First, we use variable transformation to transform the equation into an new equation which is defined in [-1,1]. Then, with the help of Gronwall inequality and some other lemmas, we provide a rigorous error analysis for the proposed method, which shows that the numerical error decay exponentially in L~∞ and L_(ω~c)~2-norm. In the end, we give numerical test to confirm the conclusion.展开更多
In this paper, we present a numerical method for solving two-dimensional VolterraFredholm integral equations of the second kind(2DV-FK2). Our method is based on approximating unknown function with Bernstein polynomial...In this paper, we present a numerical method for solving two-dimensional VolterraFredholm integral equations of the second kind(2DV-FK2). Our method is based on approximating unknown function with Bernstein polynomials. We obtain an error bound for this method and employ the method on some numerical tests to show the efficiency of the method.展开更多
文摘In this paper, we establish first a vector integro-differential inequality. Then by using the intequlity and the variation of constants formula to obtain some sufficient algebraic criteria for the stability and periodic solutions of a class of Volterra integro-differential largo-scale systems. Finally, some simple examples of application are given.
基金supported by the State Key Program of National Natural Science Foundation of China(11931003)the National Natural Science Foundation of China(41974133,11671157)。
文摘In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.
基金supported by the National Natural Science Foundation of China(11161018)the NSF of Guangxi Zhuang Autonomous Region(2012GXNSFAA053009)+3 种基金the NSF of Guangdong Province(s2013010013385)the Science Innovation Project of Department of Education of Guangdong province(2013KJCX0125)the NSFP of Zhanjiang Normal University(ZL1303)the Innovation and Developing School Project of Department of Education of Guangdong province(2014KZDXM065)
文摘研究了一类新的非线性时滞Volterra-Fredholm型积分不等式.该不等式把文献[Ma,QH,Pecaric,J:Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type integral inequalities.Nonlinear Anal.69(2008)393-407]中的函数σ_1(s)推广成函数w(u(s))f(s),其中w(u(s))是未知函数与非线性函数的复合函数.利用变量替换、放大及常量与变量的辩证关系等方法给出了该不等式中未知函数的估计.最后,用所得结果给出了一类积分方程解的估计.
基金The research supported by the National Natural Science Foundation of China.
文摘This paper deals with the existence of positive periodic solutions for a kind of nonautonomous Volterra intergo-differential equations by employing the Krasnoselskii fixed point theorem. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results.
基金supported by National Science Foundation of China(11671157,11626074)Hanshan Normal Uninversity projects(LF201404,Z16027)
文摘In this article, we study the Volterra integral equations with two kinds of delay that are proportional delay and nonproportional delay. We mainly use Chebyshev spectral collocation method to analyze them. First, we use variable transformation to transform the equation into an new equation which is defined in [-1,1]. Then, with the help of Gronwall inequality and some other lemmas, we provide a rigorous error analysis for the proposed method, which shows that the numerical error decay exponentially in L~∞ and L_(ω~c)~2-norm. In the end, we give numerical test to confirm the conclusion.
基金Supported by the Center of Excellence for Mathematics,Shahrekord University,Iran
文摘In this paper, we present a numerical method for solving two-dimensional VolterraFredholm integral equations of the second kind(2DV-FK2). Our method is based on approximating unknown function with Bernstein polynomials. We obtain an error bound for this method and employ the method on some numerical tests to show the efficiency of the method.
