A Numerical Study for the Dirichlet Problem of the Helmholtz Equation
Mathematics, 2021 In this paper, an effective numerical method for the Dirichlet problem connected with the Helmholtz equation is proposed. We choose a single-layer potential approach to obtain the boundary integral equation with the density function, and then we deal ...
Yao Sun, Shijie Hao
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A new technical for solving a weakly singular integro-differential equations
Journal of Taibah University for Science, 2017 In this work, we transform a weakly singular integro-differential equations with logarithmic kernel to singular integral equations of Cauchy type and we prove by regularization the existence and uniqueness of the solution of this equations.
Mostefa Nadir
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The Szegő kernel as a singular integral kernel on a family of weakly pseudoconvex domains [PDF]
Transactions of the American Mathematical Society, 1987 The Szegö kernels on the weakly pseudoconvex domains { Im
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A Regularization of Fredholm type singular integral equations
International Journal of Mathematics and Mathematical Sciences, 2001 We present a method to regularize first and second kind integral equations of Fredholm type with singular kernel. By appropriate application of the Poincaré-Bertrand formula we change such integral equations into a second kind Fredholm's integral ...
N. Aliev, S. Mohammad Hosseini
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On multi-singular integral equations involving n weakly singular kernels
Filomat, 2018 We deal with some sources of Banach spaces which are closely related to an important issue in applied mathematics i.e. the problem of existence and uniqueness of the solution for the very applicable weakly singular integral equations. In the classical mode, the uniform space (C[a,b], ||.||?) is usually applied to the related discussion ...
Sales, S. M. S. Nabavi, Baghani, O.
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analysis of Product Integration Methods for a Class of Singular Volterra Integral Equations
Trends in Computational and Applied Mathematics, 2000 The construction and analysis of high order numerical methods for Volterra integral equations with a certain weakly singular kernel have been investigated in [6], under the assumption the the solution is sufficiently smooth.
T. Diogo, P. Lima, N.B. Franco
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Smoothness of Solutions of Volterra Integral Equations with Weakly Singular Kernels [PDF]
SIAM Journal on Mathematical Analysis, 1971 Differentiability of nonlinear Volterra integral equations of second kind with convolutional weakly singular ...
Miller, Richard K., Feldstein, Alan
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Journal of Inequalities and Applications, 2016 Some new inequalities with weakly singular integral kernel are developed, which generalize some known inequalities and can be used in the qualitative and quantitative analysis of the solutions to certain fractional differential equations.
Run Xu, Fanwei Meng
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Design of quadrature rules for Müntz and Müntz-logarithmic polynomials using monomial transformation [PDF]
, 2009 A method for constructing the exact quadratures for Müntz and Müntz-logarithmic polynomials is presented. The algorithm does permit to anticipate the precision (machine precision) of the numerical integration of Müntz-logarithmic polynomials in terms of ...
Lombardi, Guido
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The Combined Reproducing Kernel Method and Taylor Series for Solving Weakly Singular Fredholm Integral Equations [PDF]
, 2016 In this paper, a numerical method is proposed for solving weakly singular Fredholm integral equations in Hilbert reproducing kernel space (RKHS). The Taylor series is used to remove singularity and reproducing kernel function are used as a basis.
Alvandi, Azizallah, Paripour, Mahmoud
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