Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions
Farshid Mirzaee,Sima Piroozfar +1 more
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TLDR
In this paper, the authors developed two-dimensional triangular orthogonal functions (2D-TFs) for numerical solution of the linear 2D Fredholm integral equations of the second kind.About:
This article is published in Journal of King Saud University - Science.The article was published on 2010-10-01 and is currently open access. It has received 27 citations till now. The article focuses on the topics: Fredholm integral equation & Fredholm theory.read more
Citations
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Numerical solutions of nonlinear two-dimensional partial Volterra integro-differential equations by Haar wavelet
TL;DR: A non-linear kernel comprising a function of partial derivatives of arbitrary order is approximated by Theorem 2 in Ref.
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A computational method based on hybrid of block-pulse functions and Taylor series for solving two-dimensional nonlinear integral equations
TL;DR: In this paper, a new reliable technique, which is based on hybrid functions approximation, is introduced for the approximate solutions of two-dimensional nonlinear Fredholm and Volterra integral equations.
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Solution of Two-dimensional Fredholm Integral Equation via RBF-triangular Method
TL;DR: In this paper, a new method is introduced to solve a two-dimensional Fredholm integral equation, which is based on the approximation by Gaussian radial basis functions and triangular nodes and weights.
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A Novel Numerical Method of Two-Dimensional Fredholm Integral Equations of the Second Kind
Yanying Ma,Jin Huang,Hu Li +2 more
TL;DR: In this article, a novel numerical method is developed for solving two-dimensional linear Fredholm integral equations of the second kind by integral mean value theorem, where each element of the generated discrete matrix is not required to calculate integrals, and the approximate integral operator is convergent according to collectively compact theory.
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A numerical method for solvability of some non-linear functional integral equations
TL;DR: In this article, the existence of solution for non-linear functional integral equations of two variables in Banach algebra C ( [ 0, b ] [ 0, c ], R ), b, c > 0 was proved.
References
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Book
The Numerical Solution of Integral Equations of the Second Kind
TL;DR: In this paper, a brief discussion of integral equations is given, and the Nystrom method is used to solve multivariable integral equations on a piecewise smooth planar boundary.
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A survey of numerical methods for the solution of Fredholm integral equations of the second kind
Lars B. Wahlbin,Kendall Atkinson +1 more
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Wavelet-like bases for the fast solutions of second-kind integral equations
TL;DR: In this article, a class of vector-space bases is introduced for sparse representation of discretizations of integral operators, where an operator with a smooth, nonoscillatory kernel possessing a finite number of singularities in each row or column is represented in these bases as a sparse matrix, to high precision.
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A new set of orthogonal functions and its application to the analysis of dynamic systems
TL;DR: It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.
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