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Numerical Methods for Solving Fredholm Integral Equations of Second Kind [PDF]
Abstract and Applied Analysis, 2013 Integral equation has been one of the essential tools for various areas of applied mathematics. In this paper, we review different numerical methods for solving both linear and nonlinear Fredholm integral equations of second kind.
S. Saha Ray, P. K. Sahu
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Probabilistic Analysis of Numerical Methods for Integral Equations
Journal of Integral Equations and Applications, 1991 Numerical problems and algorithms for solving Fredholm integral equations are analyzed from a probabilistic point of view. The probability measures on the set of right-hand sides and on the set of kernels are fixed. The author uses Wiener type measures which are naturally related to the scale of Sobolev spaces.
S. Heinrich
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Numerical methods for integral equations of Mellin type
Journal of Computational and Applied Mathematics, 2000 We present a survey of numerical methods (based on piecewise polynomial approximation) for integral equations of Mellin type, including examples arising in boundary integral methods for partial differential equations on polygonal domains.
Elschner, Johannes, Graham, Ivan G.
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A Survey of Numerical Methods for Solving Nonlinear Integral Equations
Journal of Integral Equations and Applications, 1992 The author gives a survey of numerical methods for solving nonlinear integral equations of the second kind such as the following: \[ x(t)=y(t)+\int_ D K(t,s)f(s,x(s))ds,\quad t\in D. \] Projection methods (such as Nyström technique and iterated projection method) are described and convergence results are given.
K. Atkinson
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Numerical integration methods for the solution of singular integral equations [PDF]
Quarterly of Applied Mathematics, 1977 The evaluation of the stress intensity factors at the tips of a crack in a homogeneous isotropic and elastic medium may be achieved with higher accuracy and much less computation if the Lobatto-Chebyshev method of numerical solution of the corresponding system of singular integral equations is used instead of the method of Gauss-Chebyshev commonly ...
Theocaris, P. S., Ioakimidis, N. I.
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Numerical methods for stochastic Volterra integral equations with weakly singular kernels [PDF]
IMA Journal of Numerical Analysis, 2020 In this paper we first establish the existence, uniqueness and Hölder continuity of the solution to stochastic Volterra integral equations (SVIEs) with weakly singular kernels, with singularities $\alpha \in (0, 1)$ for the drift term and $\beta \in (0,
Min Li, Chengming Huang, Yaozhong Hu
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A numerical method for multidimensional Volterra integral equations
Applied Mathematical Sciences, 2022 In this paper, we introduce a new numerical procedure to solve multi-dimensional Volterra integral equations, based on the weighted mean-value theorem. Our method allows to determine a system of nonlinear equations, where the rst one is obtained via the application of the theoretical results, and the remaining ones are built through a Picard-like ...
Immacolata Oliva +1 more
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Methods and effective algorithms for solving multidimensional integral equations
Российский технологический журнал, 2022 Objectives. Integral equations have long been used in mathematical physics to demonstrate existence and uniqueness theorems for solving boundary value problems for differential equations. However, despite integral equations have a number of advantages in
A. B. Samokhin
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Certain results associated with mixed integral equations and their comparison via numerical methods
Journal of Umm Al-Qura University for Applied Sciences, 2022 In this article, we consider existence and unique of solutions of linear mixed integral equations of third, second and first kinds. Then, we use the collection method to discuss numerical solutions by employing Chebyshev and Legendre polynomials.
S. Alhazmi
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Numerical Method for Fractional Fuzzy Integral Equations [PDF]
, 2021 Abstract In the present work we construct an iterative method for the numerical solution of fuzzy fractional Volterra integral equations, by using the technique of fuzzy product integration. The existence and uniqueness of the solution and the uniform boundedness of the terms of the Picard iterations are proved. The convergence of the iterative
Alexandru Mihai Bica +2 more
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