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Solving a Singular Integral Equation
Computational Mathematics and Modeling, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2012
The theory introduced in previous chapters, especially the Fredholm Theory, was presented under the restrictive assumptions that the kernel was continuous on its domain of definition and that the interval of integration was finite. There is no guarantee that those results or similar ones will hold if the kernel has an infinite discontinuity or if the ...
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The theory introduced in previous chapters, especially the Fredholm Theory, was presented under the restrictive assumptions that the kernel was continuous on its domain of definition and that the interval of integration was finite. There is no guarantee that those results or similar ones will hold if the kernel has an infinite discontinuity or if the ...
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1989
In this chapter we will consider one-dimensional singular integral equations involving Cauchy principal values that arise from boundary value problems for holomorphic functions. The investigations of these integral equations with Cauchy kernels by Gakhov, Muskhelishvili, Vekua, and others have had a great impact on the further development of the ...
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In this chapter we will consider one-dimensional singular integral equations involving Cauchy principal values that arise from boundary value problems for holomorphic functions. The investigations of these integral equations with Cauchy kernels by Gakhov, Muskhelishvili, Vekua, and others have had a great impact on the further development of the ...
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Modifid Interpolatory Projection Method for Weakly Singular Integral Equation Eigenvalue Problems
Acta Mathematicae Applicatae Sinica (English Series), 2019Xin Zhang, Yun He
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Uniform Wavelet-Approximation of Singular Integral Equation Solutions
Lobachevskii Journal of Mathematics, 2018L. E. Khairullina, A. V. Ozhegova
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Abel’s Integral Equation and Singular Integral Equations
2011Abel’s integral equation occurs in many branches of scientific fields [1], such as microscopy, seismology, radio astronomy, electron emission, atomic scattering, radar ranging, plasma diagnostics, X-ray radiography, and optical fiber evaluation. Abel’s integral equation is the earliest example of an integral equation [2].
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Product Integration for Singular Integrals and Singular Integral Equations
1979Integral equations with weakly singular kernels often have solutions which have derivative singularities at the end points of the range of integration. The error analysis of a product integration method for such integral equations depends on the error analysis of the product integration method applied to integrals of the form \(\int\limits_0^1 {g\left(
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A spectral collocation method for a weakly singular Volterra integral equation of the second kind
Advances in Computational Mathematics, 2016Can Huang, M. Stynes
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Integrable Singular Integral Evolution Equations
1993Integro-differential evolution equations (IDEE’s) appear in several areas of applied Science. For instance, in a fluid dynamical context, equation $$\begin{array}{*{20}{c}} {{{u}_{t}} + au{{u}_{x}} + \int\limits_{{ - \infty }}^{\infty } {dx\prime K(x - x\prime ){{u}_{{x\prime }}}(x\prime ,t) = 0,} } & {K(x): = \int\limits_{{ - \infty }}^{\infty } {\
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