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Newton-Krylov generalized minimal residual algorithm in solving nonlinear Volterra-Fredholm-Hammerstein integral equations [PDF]

Mathematics and Computational Sciences, 2021
In this paper, Galerkin and collocation methods based on shifted Legendre polynomials and spectral methods have been applied on nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations, these methods transfer the finding solution of a nonlinear ...
Ahmad Zavvartorbati
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Lyapunov Functionals in Integral Equations

Axioms, 2023
Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it is therefore further explored in this paper.
Youssef N. Raffoul, Joseph Raffoul
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Plane wave scattering from thin dielectric disk in free space: Generalized boundary conditions, regularizing Galerkin technique and whispering gallery mode resonances

IET Microwaves, Antennas & Propagation, 2021
Considered is the plane‐wave scattering from and absorption by a thin circular dielectric disk. The analysis uses a set of the singular integral equations for the effective electric and magnetic currents, derived using the generalized boundary conditions
Mario Lucido, Mykhaylo V. Balaban, Alexander I. Nosich   +2 more
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The Solution of Generalization of the First and Second Kind of Abel’s Integral Equation

JTAM (Jurnal Teori dan Aplikasi Matematika), 2023
Integral equations are equations in which the unknown function is found to be inside the integral sign. N. H. Abel used the integral equation to analyze the relationship between kinetic energy and potential energy in a falling object, expressed by two ...
Muhammad Taufik Abdillah, Berlian Setiawaty, Sugi Guritman   +2 more
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Solving linear and nonlinear Volterra Fuzzy Integral Equations System via Differential Transform Method

Fuzzy Optimization and Modeling, 2022
In this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM).
Mahmoud Paripour, Mandana Takrimi
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Non-homogeneous impulsive time fractional heat conduction equation

Journal of Numerical Analysis and Approximation Theory, 2023
This article provides a concise exposition of the integral transforms and its application to singular integral equation and fractional partial differential equations.
Arman Aghili
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Solution of Fractional Delay Linear Integro-differential Equations Using Variational Approach and Approximate method

Journal of Kufa for Mathematics and Computer, 2013
In this paper fractional linear integro-differential equations with and without delays is studied, and solving such equations by using the variational approach and singularity methods.    
Fadhel Subhi Fadhel, Saad Naji Al-Azawi, Thekra Abdul Latiff Ibrahem   +2 more
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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

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, Shiqing Zhang, Futian Weng, Hongli Sun   +3 more
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A problem with shift for a mixed-type model equation of the second kind in an unbounded domain

Қарағанды университетінің хабаршысы. Математика сериясы, 2022
This article studies a problem with shift in the characteristics of different families in an unbounded domain for a mixed-type model equation of the second kind.
R.T. Zunnunov, A.A. Ergashev
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On the approximate solution of nonlinear singular integral equations with positive index

International Journal of Mathematics and Mathematical Sciences, 1996
This paper is devoted to investigating a class of nonlinear singular integral equations with a positive index on a simple closed smooth Jordan curve by the collocation method.
S. M. Amer
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