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SUPERCONVERGENCE OF GENERALIZED DIFFERENCE METHOD FOR ELLIPTIC BOUNDARY VALUE PROBLEM 被引量:2
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作者 陈仲英 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1994年第2期163-171,共9页
Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that fo... Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method. 展开更多
关键词 SUPERCONVERGENCE generalized DIFFERENCE method ELLIPTIC boundary value problem
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BOUNDARY VALUE PROBLEM FOR A GENERALIZED LINARD EQUATION 被引量:2
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作者 LiuBing YuJianshe 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第1期31-38,共8页
By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>... By coincidence degree,the existence of solution to the boundary value problem of a generalized Liénard equationa(t)x'+F(x,x′)x′+g(x)=e(t), x(0)=x(2π),x′(0)=x′(2π)is proved,where a∈C 1[0,2π],a(t)>0(0≤t≤2π),a(0)=a(2π),F(x,y)=f(x)+α|y| β,α>0,β>0 are all constants,f∈C(R,R),e∈C[0,2π]. An example is given as an application. 展开更多
关键词 coincidence degree boundary value problem generalized Liénard equation existence.
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THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS 被引量:2
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作者 司中伟 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2013年第2期393-403,共11页
Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej+ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f sati... Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej+ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 1, - ……, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn+1 will be investigated. 展开更多
关键词 generalized analytic function Hilbert boundary value problem H^u function
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Generalized variational principles for boundary value problem of electromagnetic field in electrodynamics 被引量:1
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作者 刘彬 王作君 郑世科 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第4期471-480,共10页
An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien's method, a pair of generalized variational principl... An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien's method, a pair of generalized variational principles (GVPs) are established, which directly leads to all four Maxwell's equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem. 展开更多
关键词 generalized variational principle (GVP) electromagnetic field ELECTRODYNAMICS boundary value problem finite element method
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Free boundary value problems for a class of generalized diffusion equation 被引量:1
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作者 LiancunZheng XinxinZhang 《Journal of University of Science and Technology Beijing》 CSCD 2002年第6期422-425,共4页
The transport behavior of free boundary value problems for a class ofgeneralized diffusion equations was studied. Suitable similarity transformations were used toconvert the problems into a class of singular nonlinear... The transport behavior of free boundary value problems for a class ofgeneralized diffusion equations was studied. Suitable similarity transformations were used toconvert the problems into a class of singular nonlinear two-point boundary value problems andsimilarity solutions were numerical presented for different representations of heat conductionfunction, convection function, heat flux function, and power law parameters by utilizing theshooting technique. The results revealed the flux transfer mechanism and the character as well asthe effects of parameters on the solutions. 展开更多
关键词 free boundary value problem generalized diffusion equation nonlinearboundary problem shooting technique
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Multiplicity Results for Second-order Generalized Sturm-Liouville Boundary Value Problems with Dependence on the First Order Derivative 被引量:1
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作者 SHEN Chun-fang YANG Liu LIU Xi-ping 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期114-125,共12页
By using fixed point theorems,we consider multiplicity of positive solutions for second-order generalized Sturm-Liouville boundary value problem,where the first order derivative is involved in the nonlinear term expli... By using fixed point theorems,we consider multiplicity of positive solutions for second-order generalized Sturm-Liouville boundary value problem,where the first order derivative is involved in the nonlinear term explicitly.We show the existence of multiple positive solutions for the problems.Example is given to illustrate the main results of the article. 展开更多
关键词 generalized Sturm-Liouville boundary value problem positive solution CONE fixed point
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Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions
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作者 YU De-jian 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第1期110-117,共8页
In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space whic... In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process. 展开更多
关键词 abstract kinetic equation with the first kind of critical parameter boundary value problem of abstract kinetic equation generalized periodic boundary conditions abstract linear integral operator of Volterra type integral operator solving process
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Numerical Computing for a Class of Free Multipoint Boundary Value Problem of O.D.E in the Intervention of Exchange Rate
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作者 赵连霞 朱正佑 秦成林 《Journal of Shanghai University(English Edition)》 CAS 2005年第4期320-325,共6页
In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenilla... In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenillas and Femaado Zapatero. A numerical example was given for illustrating the validity of this method. 展开更多
关键词 exchange rate interventon nonlinear ordinary differential equation free boundary value problem generalized shooting method
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Jacobi-Sobolev Orthogonal Polynomialsand Spectral Methods for Elliptic Boundary Value Problems
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作者 Xuhong Yu Zhongqing Wang Huiyuan Li 《Communications on Applied Mathematics and Computation》 2019年第2期283-308,共26页
Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet ... Generalized Jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized Jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the Jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated Jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy. 展开更多
关键词 generalized JACOBI POLYNOMIALS Spectral method - Jacobi-Sobolev ORTHOGONAL BASIS functions ELLIPTIC boundary value problems Error analysis
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Monotone Iterative Method for Set valued Quasilinear Elliptic Boundary Value Problems
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作者 孙乐林 徐迪红 +1 位作者 程建 李荣华 《Northeastern Mathematical Journal》 CSCD 2001年第1期5-8,共4页
关键词 set valued differential equation elliptic boundary value problem generalized monotone iteration
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INHOMOGENEOUS INITIAL-BOUNDARY VALUE PROBLEM FOR GINZBURG-LANDAU EQUATIONS
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作者 杨灵娥 郭柏灵 徐海祥 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第4期373-380,共8页
Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative an... Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit. 展开更多
关键词 generalized Ginzburg-Landau equation inhomogeneous initial-boundary value problem weak solution global existence
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Boundary value problems of discrete generalized Emden-Fowler equation 被引量:14
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作者 YU Jianshe GUO Zhiming 《Science China Mathematics》 SCIE 2006年第10期1303-1314,共12页
By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp... By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established. 展开更多
关键词 DISCRETE generalized EMDEN-FOWLER equation boundary value problem SADDLE Point Theorem DISCRETE VARIATIONAL theory.
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The Initial, Boundary Value Problems for a Class of Generalized Diffusion Equations 被引量:1
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作者 Liancun ZHENG Xinxin ZHANG Jicheng HE 《Journal of Thermal Science》 SCIE EI CAS CSCD 2002年第1期31-34,共4页
The behavior for a class of initial, boundary value problems of generalized diffusion equations was studied utilizing the similarity transformation and shooting technique. Numerical solutions are presented fork(s) = S... The behavior for a class of initial, boundary value problems of generalized diffusion equations was studied utilizing the similarity transformation and shooting technique. Numerical solutions are presented fork(s) = SM exponent M 1.0 to 5.0, and power law parameter N (N = 0.3 to 3.0). The results shown that for each fixed M, the temperature distribution e decreases with increasing in power law parameter N, and for each fixed N, the temperature distribution 6 increases with the decreasing of M. 展开更多
关键词 generalized diffusion equation nonlinear boundary value problem POSITIVE solution SHOOTING technique.
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Existence of Positive Solutions of Generalized Sturm-Liouville Boundary Value Problems for a Singular Differential Equation 被引量:1
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作者 Jing Bao YANG1, Zhong Li WEI2,3 1. Department of Sciences, Bozhou Teachers College, Anhui 233500, P. R. China 2. School of Sciences, Shandong Jianzhu University, Shandong 250101, P. R. China 3. School of Mathematics, Shandong University, Shandong 250100, P. R. China 《Journal of Mathematical Research and Exposition》 CSCD 2011年第5期801-813,共13页
By employing the fixed point theorem of cone expansion and compression of norm type, we investigate the existence of positive solutions of generalized Sturm-Liouville boundary value problems for a nonlinear singular d... By employing the fixed point theorem of cone expansion and compression of norm type, we investigate the existence of positive solutions of generalized Sturm-Liouville boundary value problems for a nonlinear singular differential equation with a parameter. Some sufficient conditions for the existence of positive solutions are established. In the last section, an example is presented to illustrate the applications of our main results. 展开更多
关键词 generalized Sturm-Liouville boundary value problems second-order differential equations positive solutions.
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ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS
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作者 尚亚东 郭柏灵 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第10期1168-1183,共16页
The Chebyshev pseudospectral approximation of the homogeneous initial boundary value problem for a class of multi-dimensional generalized symmetric regularized long wave (SRLW) equations is considered. The fully discr... The Chebyshev pseudospectral approximation of the homogeneous initial boundary value problem for a class of multi-dimensional generalized symmetric regularized long wave (SRLW) equations is considered. The fully discrete Chebyshev pseudospectral scheme is constructed. The convergence of the approximation solution and the optimum error of approximation solution are obtained. 展开更多
关键词 multi-dimensional generalized SRLW equation initial and boundary value problem Chebyshev pseudospectral method error estimate
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BLOW-UP AND DIE-OUT OF SOLUTIONS OF NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS OF GENERALIZED NERVE CONDUCTION TYPE
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作者 王凡彬 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第11期1101-1106,共6页
This paper considers the initial boundary value problems with three types of the boundary conditions for nonlinear pseudo-hyperbolic equations of generalized nerve conduction type, using foe eigenfunction method, ... This paper considers the initial boundary value problems with three types of the boundary conditions for nonlinear pseudo-hyperbolic equations of generalized nerve conduction type, using foe eigenfunction method, the conditions for which the solutions blow-up and die-out in the finile time are got. 展开更多
关键词 nonlinear pseudo-hyperbolic equation of generalized nerve conduction type initial boundary value problem eigenfunction method BLOW-UP die-out
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INITIAL BOUNDARY VALUE PROBLEM FOR GENERALIZED 2D COMPLEX GINZBURG-LANDAU EQUATION
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作者 Fu Yiping Li Yongsheng 《Journal of Partial Differential Equations》 2007年第1期65-70,共6页
In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables (2D). Applying the notion of the ε-regular map we show the unique existence of ... In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables (2D). Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor. 展开更多
关键词 generalized 2D Ginzburg-Landau equation initial boundary value problem ε-regular map global solution global attractor.
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ANTI-PERIODIC BOUNDARY VALUE PROBLEM FOR FIRST ORDER DELAY DIFFERENTIAL EQUATIONS
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作者 齐素英 李建全 《Annals of Differential Equations》 2003年第3期384-390,共7页
The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results on the existence and uniqueness of the solution for anti-periodic boundary value problem ... The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results on the existence and uniqueness of the solution for anti-periodic boundary value problem of delay differential equations. 展开更多
关键词 anti-periodic boundary value problem monotone iterative technique lower and upper related solutions delay differential equations
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ANTI-PERIODIC BOUNDARY VALUE PROBLEM FOR FUNCTIONAL DIFFENERTIAL EQUATION
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作者 Jia Ming Shen Jianhua 《Annals of Differential Equations》 2006年第4期496-501,共6页
By using upper and lower solutions coupled with monotone iterative technique, we discuss the anti-periodic boundary value problem for first order functional diffenertial equation. A sufficient condition for the existe... By using upper and lower solutions coupled with monotone iterative technique, we discuss the anti-periodic boundary value problem for first order functional diffenertial equation. A sufficient condition for the existence of the solution is obtained. 展开更多
关键词 anti-periodic boundary value problem monotone iterations the weakly lower and upper solution
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PROBABILISTIC APPROACH TO SEMILINEAR AND GENERALIZED MIXED BOUNDARY VALUE PROBLEMS
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作者 马志明 宋仁明 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1992年第3期214-228,共15页
A probabilistic approach is developed to solve semilinear and generalized mixed boundaryvalue problems involving Schrodinger operators. The results obtained in this paper generalize thecorresponding results of [1] and... A probabilistic approach is developed to solve semilinear and generalized mixed boundaryvalue problems involving Schrodinger operators. The results obtained in this paper generalize thecorresponding results of [1] and partly generalize the result of [2] as well. 展开更多
关键词 PROBABILISTIC APPROACH TO SEMILINEAR AND generalized MIXED boundary value problemS
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