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ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS
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作者 杜志华 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2007年第2期301-307,共7页
In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equation... In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu. 展开更多
关键词 Direct method of solution integral operator associate conditions of solvability characteristic singular singular integral equations
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AN OPERATORIAL APPROACH TO SINGULAR INTEGRAL EQUATIONS OF A MODIFIED TYPE
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作者 贺福利 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2008年第4期763-769,共7页
In this article,the authors discuss a kind of modified singular integral equations on a disjoint union of closed contours or a disjoint union of open arcs.The authors introduce some singular integral operators associa... In this article,the authors discuss a kind of modified singular integral equations on a disjoint union of closed contours or a disjoint union of open arcs.The authors introduce some singular integral operators associated with this kind of singular integral equations,and obtain some useful properties for them.An operatorial approach is also given together with some illustrated examples. 展开更多
关键词 singular integral equations singular integral operators operatorial approach
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Direct Solutions of Some Singular Integral Equations on the Building Domain of Complex Biballs
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作者 GONG Ding-dong GUO Yu-qin 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第1期39-44,共6页
By means of the method of solid angle coefficients and the permutation formula on the building domain of complex biballs,direct solutions of some singular integral equations with variable coefficients are discussed an... By means of the method of solid angle coefficients and the permutation formula on the building domain of complex biballs,direct solutions of some singular integral equations with variable coefficients are discussed and the explicit formulas for these solutions are obtained. 展开更多
关键词 the building domain of complex biballs solid angle coefficients singular integral equations with variable coefficients explicit solutions
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SINGULAR INTEGRAL EQUATIONS IN ORLICZ SPACES (Ⅱ)
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作者 邓耀华 《Acta Mathematica Scientia》 SCIE CSCD 1989年第2期215-226,共12页
The singular integral equations with Cauchy kernels have studied in L_p(Γ),p>1,in detail.Here Γ stands for the set of a finite number of closed Liapunoff's curves which have no common points and T denotes the... The singular integral equations with Cauchy kernels have studied in L_p(Γ),p>1,in detail.Here Γ stands for the set of a finite number of closed Liapunoff's curves which have no common points and T denotes the completely continuous operator in the space sunder consideration. In this paper, we consider the equations mentioned above in Orlicz spaces L_M(Γ). It is proved that the Nether theorem and the index formula are hold true in the case of reflexive Orlicz spaces. 展开更多
关键词 singular integral equations IN ORLICZ SPACES 七云
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SINGULAR INTEGRAL EQUATIONS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER 被引量:5
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作者 钟寿国 《Acta Mathematica Scientia》 SCIE CSCD 2005年第2期193-200,共8页
In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and th... In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given. 展开更多
关键词 Open arc singular integral equation solutions with singularity of higher order Noether theorem characteristic equation
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SINGULAR INTEGRAL EQUATIONS WITH COSECANT KERNEL IN SOLUTIONS WITH SINGULARITIES OF ORDER ONE 被引量:2
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作者 代晋军 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2006年第3期410-414,共5页
In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc t-t0/a along closed smooth contours restricted i... In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc t-t0/a along closed smooth contours restricted in the strip 0 〈 Rez 〈 aπ is discussed. Finally, the solutions with singularities of order one for the above two problems are discussed. 展开更多
关键词 Cosecant kernel singular integral equation the singularities of order one
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SINGULAR INTEGRAL EQUATIONS ON THE REAL AXIS WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER 被引量:1
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作者 钟寿国 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1093-1099,共7页
We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with sol... We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by this article contain special cases discussed before. 展开更多
关键词 singular integral equation solution with singularities of higher order real axis infinite point class ■*λ1 ... λn λ∞
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SINGULAR INTEGRAL EQUATIONS WITHCOMPLEX TRANSLATIONS 被引量:1
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作者 杜金元 胡继承 《Acta Mathematica Scientia》 SCIE CSCD 1999年第4期469-480,共12页
In this paper, a class of singular integral equations with complex translations is discussed. By using the Plemelj projection method the authors reduce them to the boundary value problem of analytic functions in A(+)(... In this paper, a class of singular integral equations with complex translations is discussed. By using the Plemelj projection method the authors reduce them to the boundary value problem of analytic functions in A(+)(H) over cap(0) with upper translation and the boundary value problem of analytic functions in A-(H) over cap(0) with lower translation, which are solved here. 展开更多
关键词 singular integral equation singular integral operator singular projection operator upper translation lower translation
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The Method of Solutions for some Kinds of Singular Integral Equations of Convolution Type with Both Reflection and Translation Shift 被引量:1
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作者 LI Ping-run 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第1期107-115,共9页
In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coeffici... In this paper,some kinds of singular integral equations of convolution type with reflection and translation shift are discussed and they are turned into Riemann boundary value problems with both discontinuous coefficients and reflection by using the Fourier transform.In spite of the classical method for solution,we are to give another method,therefore the general solution and condition of solvability are obtained in class{0}. 展开更多
关键词 singular integral equation convolution type Riemann boundary value problem REFLECTION translation shift
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Numerical methods for solving singular integral equations obtained by fracture mechanical analysis of cracked wedge
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作者 M.GHADIRI H.GHASEMI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第3期311-324,共14页
The numerical solutions to the singular integral equations obtained by the fracture mechanical analyses of a cracked wedge under three different conditions are considered. The three considered conditions are:(i) a rad... The numerical solutions to the singular integral equations obtained by the fracture mechanical analyses of a cracked wedge under three different conditions are considered. The three considered conditions are:(i) a radial crack on a wedge with a nonfinite radius under the traction-traction boundary condition,(ii) a radial crack on a wedge with a finite radius under the traction-traction boundary condition, and(iii) a radial crack on a finite radius wedge under the traction-displacement boundary condition. According to the boundary conditions, the extracted singular integral equations have different forms. Numerical methods are used to solve the obtained coupled singular integral equations, where the Gauss-Legendre and the Gauss-Chebyshev polynomials are used to approximate the responses of the singular integral equations. The results are presented in figures and compared with those obtained by the analytical response. The results show that the obtained Gauss-Chebyshev polynomial response is closer to the analytical response. 展开更多
关键词 fracture mechanics NUMERICAL ANALYTICAL singular integral equation Gauss-Legendre
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SINGULAR INTEGRAL EQUATIONS AND BOUNDARY ELEMENT METHOD OF CRACKS IN THERMALLY STRESSED PLANAR SOLIDS
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作者 徐春晖 秦太验 华云龙 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第4期399-406,共8页
Using the method of the boundary integral equation, a set of singular integral equations of the hear transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, a... Using the method of the boundary integral equation, a set of singular integral equations of the hear transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, and then,its numerical method is proposed by the numerical method of the singular integral equations combined with boundary element method. Moreover, the singular nature of temperature gradient field near the crack front is proved by the main-part analysis method of the singular integral equation, and the singular temperature gradients are exactly obtained. Finally, several typical examples calculated. 展开更多
关键词 heat transfer CRACK singular integral equation boundary element method stress intensity factor
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TWO-DIMENSIONAL SINGULAR INTEGRAL EQUATIONS OF THE HYPERCOMPLEX FUNCTIONS
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作者 刘春根 《Acta Mathematica Scientia》 SCIE CSCD 1996年第1期44-50,共7页
In this paper, it is considered for some two-dimensional singular integral equations of the hypercomplex functions in the Douglis sense. In some special cases, the Fredholm' conditions and index formula of such eq... In this paper, it is considered for some two-dimensional singular integral equations of the hypercomplex functions in the Douglis sense. In some special cases, the Fredholm' conditions and index formula of such equations are obtained. 展开更多
关键词 singular integral equation hypercomplex function index formula
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Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order
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作者 HAN Hui-li 1,2 ,DU Jin-yuan 1,3 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China 2. School of Mathematics and Computer, Ningxia University, Yinchuan 750021, Ningxia, China 3. Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei, China 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第2期339-343,共5页
We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integratio... We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integration is in the strip 0<Rez<aπ. 展开更多
关键词 boundary value problem singular integral equation the singularities of high order
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Fast Multiscale Collocation Methods for a Class of Singular Integral Equations
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作者 张永东 陈仲英 《Northeastern Mathematical Journal》 CSCD 2006年第2期206-218,共13页
This paper develops fast multiscale collocation methods for a class of Fredholm integral equations of the second kind with singular kernels. A truncation strategy for the coefficient matrix of the corresponding discre... This paper develops fast multiscale collocation methods for a class of Fredholm integral equations of the second kind with singular kernels. A truncation strategy for the coefficient matrix of the corresponding discrete system is proposed, which forms a basis for fast algorithms. The convergence, stability and computational complexity of these algorithms are analyzed. 展开更多
关键词 multiscale method collocation method singular integral equation
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Wavelet Numerical Solutions for Weakly Singular Fredholm Integral Equations of the Second Kind 被引量:1
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作者 TANG Xinjian PANG Zhicheng +1 位作者 ZHU Tonglin LIU Jian 《Wuhan University Journal of Natural Sciences》 CAS 2007年第3期437-441,共5页
Daubechies interval cally weakly singular Fredholm kind. Utilizing the orthogonality equation is reduced into a linear wavelet is used to solve nurneriintegral equations of the second of the wavelet basis, the integra... Daubechies interval cally weakly singular Fredholm kind. Utilizing the orthogonality equation is reduced into a linear wavelet is used to solve nurneriintegral equations of the second of the wavelet basis, the integral system of equations. The vanishing moments of the wavelet make the wavelet coefficient matrices sparse, while the continuity of the derivative functions of basis overcomes naturally the singular problem of the integral solution. The uniform convergence of the approximate solution by the wavelet method is proved and the error bound is given. Finally, numerical example is presented to show the application of the wavelet method. 展开更多
关键词 weakly singular integral equations interval wavelet sparse matrix
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On a Class of Two Dimensional Singular Integral Equations
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作者 Zhang Zhong-xiang Du Jin-yuan 《Wuhan University Journal of Natural Sciences》 CAS 1999年第2期4-9,共6页
We mainly consider a class of two dimensional normal type singular integral equations, the solutions as well as the conditions of solvability of which are obtained .The methods used consist of transferring them to sev... We mainly consider a class of two dimensional normal type singular integral equations, the solutions as well as the conditions of solvability of which are obtained .The methods used consist of transferring them to several one dimensional Riemann boundary value problems, and then solving the latter. 展开更多
关键词 two dimensional singular integral equations Riemann boundary value problem
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Characteristic Singular Integral Equations with Solutions Having Singularities of Higher Order on the Real Axis 被引量:1
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作者 ZHONG Shouguo 《Wuhan University Journal of Natural Sciences》 CAS 2009年第4期299-303,共5页
Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations wi... Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter. 展开更多
关键词 characteristic singular integral equation Riemann boundary value problem (RBVP) solution with singularities of higher order real axis
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ON THE METHOD OF SOLVING TWO KINDS OF CONVOLUTION SINGULAR INTEGRAL EQUATIONS WITH REFLECTION 被引量:2
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作者 Pingrun Li 《Annals of Differential Equations》 2013年第2期159-166,共8页
In this paper, two kinds of convolution integral equations with both Cauchy kernel and reflection are discussed. Using Fourier transformation theory they can be transformed into Riemann boundary value problems with bo... In this paper, two kinds of convolution integral equations with both Cauchy kernel and reflection are discussed. Using Fourier transformation theory they can be transformed into Riemann boundary value problems with both discontinuous coefficients and reflection. And we give a new method, by which the general solution and the condition of solvability are obtained respectively. 展开更多
关键词 singular integral equation of convolution type Riemann boundary value problem Cauchy kernel REFLECTION translation shift
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Research on Chaos of Nonlinear Singular Integral Equation
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作者 Yannan Liu Yu Wang 《Journal of Applied Mathematics and Physics》 2023年第4期1152-1159,共8页
In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of... In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of solving by iterative method. 展开更多
关键词 Lagrange Interpolation Method Nonlinear singular integral Equation Iterative Method
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On the Numerical Solution of Singular Integral Equation with Degenerate Kernel Using Laguerre Polynomials
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作者 Khadeejah Sultan Alroogy Musa Adam Aigo 《American Journal of Computational Mathematics》 2023年第1期153-160,共8页
In this paper, we derive a simple and efficient matrix formulation using Laguerre polynomials to solve the singular integral equation with degenerate kernel. This method is based on replacement of the unknown function... In this paper, we derive a simple and efficient matrix formulation using Laguerre polynomials to solve the singular integral equation with degenerate kernel. This method is based on replacement of the unknown function by truncated series of well known Laguerre expansion of functions. This leads to a system of algebraic equations with Laguerre coefficients. Thus, by solving the matrix equation, the coefficients are obtained. Some numerical examples are included to demonstrate the validity and applicability of the proposed method. 展开更多
关键词 singular integral Equation Projection Method Galerkin Method La-guerre Polynomials
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