The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simpl...The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.展开更多
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
In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is t...In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L2[-π, π].展开更多
In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity an...In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity and function with singular point. The problem investigation this type integral equation at n = 2m reduce to problem investigate the Volterra type integral equation （1） for n = 2 the theory for which was constructed in [2]. In this work, we investigation integral equation （1） at = 2m ＋ 1 In this case, we investigate integral equation （1） reduction it＇s to m integral equation type [2] φ（x）＋∫xa[p1＋p2 ln（x-a/t-a）]φ（t）/t-a dt=f（x）and one the following integral equation [1] ω（x）＋p3∫xω（t）/ a t-adt=g（x）.展开更多
In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM...In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.展开更多
Analytic continuation of some classical formulas with respect to a parameter is discussed. Examples are presented. The validity of these formulas is greatly expanded. Application of these results to solving some integ...Analytic continuation of some classical formulas with respect to a parameter is discussed. Examples are presented. The validity of these formulas is greatly expanded. Application of these results to solving some integral equations with hyper-singular kernels is given.展开更多
The solutions of the nonlinear singular integral equation , t 6 L, are considered, where L is a closed contour in the complex plane, b ≠ 0 is a constant and f(t) is a polynomial. It is an extension of the results obt...The solutions of the nonlinear singular integral equation , t 6 L, are considered, where L is a closed contour in the complex plane, b ≠ 0 is a constant and f(t) is a polynomial. It is an extension of the results obtained in [1] when f(t) is a constant. Certain special cases are illustrated.展开更多
This paper is devoted to studying the approximate solution of singular integral equations by means of Chebyshev polynomials. Some examples are presented to illustrate the method.
In this article, we present approximate solution of the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (V-FIE), which is deduced by using new strategy (combined Laplace homotopy perturba...In this article, we present approximate solution of the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (V-FIE), which is deduced by using new strategy (combined Laplace homotopy perturbation method (LHPM)). Here we consider the V-FIE with Cauchy kernel. Solved examples illustrate that the proposed strategy is powerful, effective and very simple.展开更多
This paper proposes the combined Laplace-Adomian decomposition method (LADM) for solution two dimensional linear mixed integral equations of type Volterra-Fredholm with Hilbert kernel. Comparison of the obtained resul...This paper proposes the combined Laplace-Adomian decomposition method (LADM) for solution two dimensional linear mixed integral equations of type Volterra-Fredholm with Hilbert kernel. Comparison of the obtained results with those obtained by the Toeplitz matrix method (TMM) demonstrates that the proposed technique is powerful and simple.展开更多
For domains composed by balls in C^n, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smoot...For domains composed by balls in C^n, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain.展开更多
After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions f...After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation展开更多
In this paper, a user friendly algorithm based on the variational iteration method (VIM) is proposed to solve singular integral equations with generalized Abel’s kernel. It is observed that an approximate solutions y...In this paper, a user friendly algorithm based on the variational iteration method (VIM) is proposed to solve singular integral equations with generalized Abel’s kernel. It is observed that an approximate solutions yn(x) converges to the exact solution irrespective of the initial choice y0 (x). Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the method in solving these types of singular integral equations.展开更多
Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds...Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.展开更多
文摘The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.
基金Supported by the National Natural Science Foundation of China (19971064)
文摘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.
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L2[-π, π].
文摘In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity and function with singular point. The problem investigation this type integral equation at n = 2m reduce to problem investigate the Volterra type integral equation （1） for n = 2 the theory for which was constructed in [2]. In this work, we investigation integral equation （1） at = 2m ＋ 1 In this case, we investigate integral equation （1） reduction it＇s to m integral equation type [2] φ（x）＋∫xa[p1＋p2 ln（x-a/t-a）]φ（t）/t-a dt=f（x）and one the following integral equation [1] ω（x）＋p3∫xω（t）/ a t-adt=g（x）.
文摘In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.
文摘Analytic continuation of some classical formulas with respect to a parameter is discussed. Examples are presented. The validity of these formulas is greatly expanded. Application of these results to solving some integral equations with hyper-singular kernels is given.
文摘The solutions of the nonlinear singular integral equation , t 6 L, are considered, where L is a closed contour in the complex plane, b ≠ 0 is a constant and f(t) is a polynomial. It is an extension of the results obtained in [1] when f(t) is a constant. Certain special cases are illustrated.
文摘This paper is devoted to studying the approximate solution of singular integral equations by means of Chebyshev polynomials. Some examples are presented to illustrate the method.
文摘In this article, we present approximate solution of the two-dimensional singular nonlinear mixed Volterra-Fredholm integral equations (V-FIE), which is deduced by using new strategy (combined Laplace homotopy perturbation method (LHPM)). Here we consider the V-FIE with Cauchy kernel. Solved examples illustrate that the proposed strategy is powerful, effective and very simple.
文摘This paper proposes the combined Laplace-Adomian decomposition method (LADM) for solution two dimensional linear mixed integral equations of type Volterra-Fredholm with Hilbert kernel. Comparison of the obtained results with those obtained by the Toeplitz matrix method (TMM) demonstrates that the proposed technique is powerful and simple.
基金Project supported by the National Science Foundation of China (10271097)
文摘For domains composed by balls in C^n, this paper studies the boundary behaviour of Cauchy type integrals with discrete holomorphic kernels and the corresponding linear singular integral equation on each piece of smooth lower dimensional edges on the boundary of the domain.
基金Supported by the National Natural Science Foundation of China( No.2 0 1980 6 33)
文摘After choosing weight functions suitably, we define a Banach spaceH ω μ (L) and discuss the generalized inverse of singular integral operators on an open arc. Using the generalized inverse, we obtain the solutions for the following singular integral equation
文摘In this paper, a user friendly algorithm based on the variational iteration method (VIM) is proposed to solve singular integral equations with generalized Abel’s kernel. It is observed that an approximate solutions yn(x) converges to the exact solution irrespective of the initial choice y0 (x). Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the method in solving these types of singular integral equations.
基金the Bilateral Science and Technology Collaboration Program of Australia 1998 the Natural Science Foundation of China (No. 1
文摘Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.
