A comparison of Newton–Raphson method with Newton–Krylov generalized minimal residual (GMRes) method for solving one and two dimensional nonlinear Fredholm integral equations

Kourosh Parand; Hafez Yari; Reza Taheri; Simin Shekarpaz

doi:10.1007/s40324-019-00196-9

A comparison of Newton–Raphson method with Newton–Krylov generalized minimal residual (GMRes) method for solving one and two dimensional nonlinear Fredholm integral equations

SeMA Journal ◽

10.1007/s40324-019-00196-9 ◽

2019 ◽

Vol 76 (4) ◽

pp. 615-624 ◽

Cited By ~ 1

Author(s):

Kourosh Parand ◽

Hafez Yari ◽

Reza Taheri ◽

Simin Shekarpaz

Keyword(s):

Integral Equations ◽

Fredholm Integral Equations ◽

Gmres Method ◽

Two Dimensional ◽

Nonlinear Fredholm Integral Equations ◽

Newton Raphson ◽

Raphson Method ◽

Minimal Residual

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Solving Two-Dimensional Nonlinear Fredholm Integral Equations Using Rationalized Haar Functions in the Complex Plane

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-019-0631-1 ◽

2019 ◽

Vol 5 (3) ◽

Author(s):

Majid Erfanian ◽

Abbas Akrami ◽

Mahmmod Parsamanesh

Keyword(s):

Integral Equations ◽

Complex Plane ◽

Fredholm Integral Equations ◽

Two Dimensional ◽

Haar Functions ◽

Nonlinear Fredholm Integral Equations

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Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm integral equations

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(00)00553-7 ◽

2001 ◽

Vol 134 (1-2) ◽

pp. 259-268 ◽

Cited By ~ 51

Author(s):

Han Guoqiang ◽

Wang Jiong

Keyword(s):

Integral Equations ◽

Fredholm Integral Equations ◽

Two Dimensional ◽

Nonlinear Fredholm Integral Equations

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Extrapolation of the Galerkin solution for two-dimensional nonlinear Fredholm integral equations with orthogonal basis of Boubaker polynomials

Computational and Applied Mathematics ◽

10.1007/s40314-021-01750-w ◽

2022 ◽

Vol 41 (1) ◽

Author(s):

Farshad Mehdifar ◽

Ali Khani

Keyword(s):

Integral Equations ◽

Orthogonal Basis ◽

Fredholm Integral Equations ◽

Two Dimensional ◽

Boubaker Polynomials ◽

Nonlinear Fredholm Integral Equations ◽

Galerkin Solution

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A new approach for numerical solution of two-dimensional nonlinear Fredholm integral equations in the most general kind of kernel, based on Bernstein polynomials and its convergence analysis

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.06.002 ◽

2018 ◽

Vol 344 ◽

pp. 482-494 ◽

Cited By ~ 8

Author(s):

A. Babaaghaie ◽

K. Maleknejad

Keyword(s):

Numerical Solution ◽

Convergence Analysis ◽

Integral Equations ◽

Bernstein Polynomials ◽

Fredholm Integral Equations ◽

Two Dimensional ◽

New Approach ◽

General Kind ◽

Nonlinear Fredholm Integral Equations

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Chebyshev Spectral Projection Methods for Two-Dimensional Fredholm Integral Equations of Second Kind

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-021-01015-4 ◽

2021 ◽

Vol 7 (3) ◽

Author(s):

Bijaya Laxmi Panigrahi ◽

Jitendra Kumar Malik

Keyword(s):

Integral Equations ◽

Spectral Projection ◽

Projection Methods ◽

Fredholm Integral Equations ◽

Two Dimensional

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Approximate solution of nonlinear Fredholm integral equations of the second kind using a class of Hermite interpolation polynomials

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2021.03.015 ◽

2021 ◽

Author(s):

Nasibeh Karamollahi ◽

Mohammad Heydari ◽

Ghasem Barid Loghmani

Keyword(s):

Approximate Solution ◽

Integral Equations ◽

Hermite Interpolation ◽

Fredholm Integral Equations ◽

Nonlinear Fredholm Integral Equations ◽

Interpolation Polynomials ◽

Hermite Interpolation Polynomials

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Discrete Legendre spectral methods for Hammerstein type weakly singular nonlinear Fredholm integral equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2021.1891225 ◽

2021 ◽

pp. 1-17

Author(s):

Moumita Mandal ◽

Kapil Kant ◽

Gnaneshwar Nelakanti

Keyword(s):

Integral Equations ◽

Spectral Methods ◽

Fredholm Integral Equations ◽

Weakly Singular ◽

Nonlinear Fredholm Integral Equations

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Solving nonlinear Fredholm integral equations with PQWs in complex plane

International Journal of Dynamical Systems and Differential Equations ◽

10.1504/ijdsde.2021.113901 ◽

2021 ◽

Vol 11 (1) ◽

pp. 18

Author(s):

H. Beiglo ◽

M. Gachpazan ◽

M. Erfanian

Keyword(s):

Integral Equations ◽

Complex Plane ◽

Fredholm Integral Equations ◽

Nonlinear Fredholm Integral Equations

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Convergence Analysis of Parabolic Basis Functions for Solving Systems of Linear and Nonlinear Fredholm Integral Equations

TURKISH JOURNAL OF MATHEMATICS ◽

10.3906/mat-1507-8 ◽

2017 ◽

Vol 41 ◽

pp. 787-796 ◽

Cited By ~ 3

Author(s):

Yousef JAFARZADEH ◽

Bagher KERAMATI

Keyword(s):

Convergence Analysis ◽

Integral Equations ◽

Basis Functions ◽

Fredholm Integral Equations ◽

Nonlinear Fredholm Integral Equations ◽

Linear And Nonlinear ◽

Parabolic Basis

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A reliable treatment to solve nonlinear Fredholm integral equations with non-separable kernel

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.113115 ◽

2020 ◽

pp. 113115

Author(s):

M.A. Hernández-Verón ◽

Eulalia Martínez ◽

Sukhjit Singh

Keyword(s):

Integral Equations ◽

Fredholm Integral Equations ◽

Separable Kernel ◽

Nonlinear Fredholm Integral Equations

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