Solving Fredholm Integral Equations Using Deep Learning. [PDF]
Int J Appl Comput Math, 2022 The aim of this paper is to provide a deep learning based method that can solve high-dimensional Fredholm integral equations. A deep residual neural network is constructed at a fixed number of collocation points selected randomly in the integration domain. The loss function of the deep residual neural network is defined as a linear least-square problem
Guan Y, Fang T, Zhang D, Jin C.
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Approximate solutions to several classes of Volterra and Fredholm integral equations using the neural network algorithm based on the sine-cosine basis function and extreme learning machine [PDF]
Frontiers in Computational Neuroscience, 2023 In this study, we investigate a new neural network method to solve Volterra and Fredholm integral equations based on the sine-cosine basis function and extreme learning machine (ELM) algorithm.
Yanfei Lu +3 more
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Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation. [PDF]
PLoS ONE, 2023 A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredholm integral ...
A Z Amin +4 more
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Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials [PDF]
The Scientific World Journal, 2014 A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation.
S. Mashayekhi, M. Razzaghi, O. Tripak
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Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem. [PDF]
Springerplus, 2016 Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis.
Altürk A.
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Advances in Difference Equations, 2020 The approximate numerical solution of the linear second kind of fuzzy integral Fredholm equations is discussed in this article. A new approach uses hybrid functions, and some useful properties of these functions are proposed to transform linear second ...
Praveen Agarwal +3 more
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A Computational Technique for Solving Three-Dimensional Mixed Volterra–Fredholm Integral Equations
Fractal and Fractional, 2023 In this article, a novel and efficient approach based on Lucas polynomials is introduced for solving three-dimensional mixed Volterra–Fredholm integral equations for the two types (3D-MVFIEK2).
A. Mahdy +3 more
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A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind
Mathematics, 2021 In this work, we present an application of Newton’s method for solving nonlinear equations in Banach spaces to a particular problem: the approximation of the inverse operators that appear in the solution of Fredholm integral equations.
José M. Gutiérrez +1 more
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Mathematical Problems in Engineering, 2022 The present paper illustrates a new numerical technique to solve a system of linear Fredholm integral equations of the second kind. The current work introduces a coupling between hybrid Bernstein functions and improved block-pulse functions (HBI).
Jihuan He +3 more
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A collocation method to the solution of nonlinear fredholm-hammerstein integral and integro-differential equation [PDF]
Journal of Hyperstructures, 2013 This paper presents a computational technique for the solution of the nonlinear Fredholm-Hammerstein integral and integrodifferential equations. A hybrid of block-pulse functions and the second kind Chebyshev polynomials (hereafter called as HBC) is used
F. Mirzaee, Elham Hadadiyan
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