Triangular functions for numerical solution of the nonlinear Volterra integral equations

Kazemi, Manochehr

doi:10.1007/s12190-021-01603-z

Cited by 10 publications

(2 citation statements)

References 33 publications

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“…But most of the works deal with the numerical analysis of functional integral equations without discussing the existence result of the solution inside its area of definition (cf. [20][21][22][23][24][25][26][27][28][29][30][31][32][33]). In this study, we examine a class of fractional-order integral equations and give a result about the existence of solutions inside their domain of definition by Petryshyn's fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

An existence result with numerical solution of nonlinear fractional integral equations

Kazemi

Deep

Nieto

2023

Math Methods in App Sciences

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By utilizing the technique of Petryshyn's fixed point theorem in Banach algebra, we examine the existence of solutions for fractional integral equations, which include as special cases of many fractional integral equations that arise in various branches of mathematical analysis and their applications. Also, the numerical iterative method is employed successfully to find the solutions to fractional integral equations. Lastly, we recall some different cases and examples to verify the applicability of our study.

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Section: Introductionmentioning

confidence: 99%

An existence result with numerical solution of nonlinear fractional integral equations

Kazemi

Deep

Nieto

2023

Math Methods in App Sciences

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“…In general, closed form analytical solutions do not exist hence numerical techniques [21,22,23,24,25,26] are being developed to tackle the most general cases that may arise from practical applications. Linear Fredholm integral equations have been discussed in [27,28,29] whereas the nonlinear Fredholm integral equation poses more challenging problem.…”

Section: Introductionmentioning

confidence: 99%

Ishikawa-Collocation Method for Nonlinear Fredholm Equations with Non-Separable Kernels

Nwaigwe

Weli²

2023

JAMCS

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A fixed point method is developed on a mesh for the solution of nonlinear Fredholm equation. First, the problem is collocated at mesh points and a second order quadrature rule is used to approximate the nonlinear integral. Under the assumption of nonexpansivity of self-map, we construct an Ishikawa iteration to linearize the resulting system and approximate the solution at the mesh points. Four numerical examples are given to verify the accuracy and practicability of the method. The results show that indeed the method converges with second order of accuracy. One important lesson from this study is that the results support the claim, in previous studies, that fixed point iterations can provide reliable means of solving several nonlinear problems. It is recommended to extend this work to functional integral equations using higher order quadrature rules.

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New iterative methods for finding solutions of Hammerstein equations

Boikanyo

Zegeye²

2022

J. Appl. Math. Comput.

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Triangular functions for numerical solution of the nonlinear Volterra integral equations

Cited by 10 publications

References 33 publications

An existence result with numerical solution of nonlinear fractional integral equations

An existence result with numerical solution of nonlinear fractional integral equations

Ishikawa-Collocation Method for Nonlinear Fredholm Equations with Non-Separable Kernels

New iterative methods for finding solutions of Hammerstein equations

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