共查询到20条相似文献,搜索用时 9 毫秒
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《Applied Mathematics Letters》2003,16(3):369-373
A quick and efficient method of solution of a singular integral equation of the first kind involving a logarithmic singularity is explained. 相似文献
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W. E. Olmstead Richard A. Handelsman 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1972,23(6):889-900
An investigation is made of the asymptotic behavior of the solutionu(t;ε) to the Volterra integral equation $$\varepsilon u(t;\varepsilon ) = \pi ^{ - \tfrac{1}{2}} \int\limits_0^t {(t - s)^{ - \tfrac{1}{2}} [f(s) - u^n (s;\varepsilon )]} ds, t \geqslant 0, n \geqslant 1$$ , in the limit as ε→0. This investigation involves a singular perturbation analysis. For the linear problem (n=1) an infinite, uniformly valid asymptotic expansion ofu(t;ε) is obtained. For the nonlinear problem (n≥2), the leading two terms of a uniformly valid expansion are found 相似文献
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Kh. Nimatov 《Siberian Mathematical Journal》1989,30(1):147-150
Kulyab, Tazik. SSR. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 1, pp. 190–193, January–February, 1989. 相似文献
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** Email: alok{at}math.iisc.ernet.in Direct function theoretic methods are developed to handle twoweakly singular integral equations with their kernels havinglogarithmic singularity. The present methods avoid the occurrenceof higher-order (or strong) singularities, like the Cauchy typesingularity in the representation of the solutions of such integralequations. 相似文献
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T. S. Polyanskaya 《Journal of Mathematical Sciences》1990,48(3):312-315
Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 44, pp. 84–88, 1985. 相似文献
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O. V. Gun’ko 《Ukrainian Mathematical Journal》2004,56(5):840-851
Using methods of the theory of boundary-value problems for analytic functions, we prove a theorem on the existence of solutions of the equation
and determine the general form of a solution by using zeros of an entire function A
2(z) of exponential type.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 695–704, May, 2004. 相似文献
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A hypersingular integral equation in two disjoint intervals is solved by using the solution of Cauchy type singular integral equation in disjoint intervals. Also a direct function theoretic method is used to determine the solution of the same hypersingular integral equation in two disjoint intervals. Solutions by both the methods are in good agreement with each other. 相似文献
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In this paper, we first discuss the midpoint rule for evaluating hypersingular integrals with the kernel sin −2[(x−s)/2] defined on a circle, and the key point is placed on its pointwise superconvergence phenomenon. We show that this phenomenon occurs when the singular point s is located at the midpoint of each subinterval and obtain the corresponding supercovergence analysis. Then we apply the rule
to construct a collocation scheme for solving the relevant hypersingular integral equation, by choosing the midpoints as the
collocation points. It’s interesting that the inverse of coefficient matrix for the resulting linear system has an explicit
expression, by which an optimal error estimate is established. At last, some numerical experiments are presented to confirm
the theoretical analysis. 相似文献
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J. J. A. M. Brands 《Applied Mathematics Letters》1990,3(4):1-4
The asymptotic behaviour for t → ∞ of ∞0 exp[tx–c(x)]dx is studied. The function c is positive and ′(x) → ∞ (x → ∞). Sufficient conditions on c are given in order that the method of Laplace is applicable. 相似文献
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《Applied Mathematics Letters》2003,16(7):1031-1037
Two quick methods of solution of a singular integral equation of the first kind defined over disjoint multiple intervals involving a logarithmic singularity are explained. 相似文献
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D. I. Sherman 《Journal of Applied Mathematics and Mechanics》1986,50(6):777-782
Certain additions are given to the theory of a singular integral equation /1/ encountered in some problems of potential theory and in a correspondingly complicated form in two-dimensional elasticity theory. 相似文献
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Ya. V. Mikityuk 《Journal of Mathematical Sciences》1992,58(6):559-562
Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 53, pp. 95–99, 1990. 相似文献
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A. V. Pskhu 《Differential Equations》2017,53(9):1160-1164
We construct an explicit representation of the solution of a multidimensional Abel integral equation of the second kind with partial fractional integrals in terms of the Wright function. 相似文献
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This paper is devoted to exact and approximate methods (first of all, direct ones) for the solution of integro-operational equations. Themost attention is paid to the theoretical substantiation of the collocation method for the solution of the mentioned equations within the general theory of approximate methods developed by L. V. Kantorovich. 相似文献