A Study of Some Iterative Methods for Solving Fuzzy Volterra-Fredholm Integral Equations

Hamoud, Ahmed A.; Azeez, Ali Dhurgham; Ghadle, Kirtiwant P.

doi:10.11591/ijeecs.v11.i3.pp1228-1235

Cited by 27 publications

(26 citation statements)

References 18 publications

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“…The auxiliary linear operator and the initial guess are chosen as (see e.g. [36][37][38][39][40] to see how HAM may work):…”

Section: Solution By Homotopy Analysis Methods (Ham)mentioning

confidence: 99%

Surprising solutions for some challenging problems arising from boundary layer theory by a new technique: the homotopy contraction mapping technique (HCMT)

Jafarimoghaddam¹

2019

SN Appl. Sci.

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In this work, the homotopy structure (1 − p)L [f ] = −p N [f ] is considered to solve some newly developed nonlinear problems in fluid dynamics. In summary, deformation in homotopy series solutions occurs from the initial trial function to the actual solution. The main challenging part in many similarity equations associated with the boundary layer theory is to identify a certain quantity of the exact solution such as f �� (0). This quantity is initially unknown and is automatically guessed through the zeroth function. Therefore, it makes sense that in the previous homotopy series solutions one would need at least another parameter i.e. the controlling parameter (ℏ) to handle the convergence through the so-called ℏ-curves analysis and eventually get an approximate value for f �� (0). Here it is accounted the basic homotopy structure with No controlling parameter (ℏ) and it is shown for the 1 st time that the zeroth order solution in homotopy series may be potential to contain some certain quantities of the exact solution, here is to be f �� (0) ; i.e. f �� 0 (0) could be f �� (0). This hypothesis is checked through a theorem, being totally linked to the Fixed Point Property (FPP), a topological invariant; i.e. being preserved by any homeomorphism. The theorem enables us Not only to check the validity of the hypothesis, but also to extract the value of the quantity as the unique description of the homotopy series solutions truncated at any order of approximation. The technique is initially introduced in a simple and straightforward manner and then it is applied to some fluid mechanical problems to be further compared with traditional homotopy analysis method, homotopy perturbation method and Numerical solutions. The outcomes indicated an excellent improvement by the present approach as only a few series terms were accounted to obtain highly accurate solutions. Keywords 3-D MHD flow • 2-D flow of UCM fluids • Homotopy analysis method (HAM) • Homotopy perturbation method (HPM) • The homotopy contraction mapping technique (HCMT)

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“…The auxiliary linear operator and the initial guess are chosen as (see e.g. [36][37][38][39][40] to see how HAM may work):…”

Section: Solution By Homotopy Analysis Methods (Ham)mentioning

confidence: 99%

Surprising solutions for some challenging problems arising from boundary layer theory by a new technique: the homotopy contraction mapping technique (HCMT)

Jafarimoghaddam¹

2019

SN Appl. Sci.

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“…A fuzzy number is generalization of a regular real number and which does not refer to a single value but rather to a connected a set of possible values, where each possible value has its weight between 0 and 1. This weight is called the membership function [9,10].…”

Section: Fuzzy Numbermentioning

confidence: 99%

Optimal Solution of Fuzzy Transshipment Problem Using Generalized Hexagonal Fuzzy Numbers

Ghadle¹,

Ingle²,

Hamoud³

2018

IJET

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In the present paper, the generalized hexagonal fuzzy number has been newly introduced to deal fuzzy transshipment problem. We solved balance and unbalance fuzzy transshipment problem by various methods. Various methods are compared to find the best solution. The objective of our paper is to find the best method for solving transshipment problem. This procedure is illustrated with numerical examples.

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“…In addition to these numerical methods, Khuri [29] used Laplace transform numerical scheme. Moreover, properties of the integro-differential equations have been studied by several authors [1,10,11,14,17,18,20,[24][25][26][27]33].…”

Section: Introductionmentioning

confidence: 99%

Laplace discrete decomposition method for solving nonlinear Volterra-Fredholm integro-differential equations

Hamoud¹,

Mohammed²

2020

J. Math. Computer Sci.

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In this article, a new modification of the Adomian Decomposition Method (ADM) that is called the Laplace Discrete Adomian Decomposition Method (LDADM) is applied to non-homogeneous nonlinear Volterra-Fredholm integro-differential equations. This method is based upon the Laplace Adomian decomposition method coupled with some quadrature rules of numerical integration. The performance of the proposed method is verified through absolute error measures between the approximated solutions and exact solutions. The series of experimental numerical results show that our proposed method performs in high accuracy and efficiency. The study highlights that the proposed method could be used to overcome the analytical approaches in solving nonlinear Volterra-Fredholm integro-differential equations.

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A Study of Some Iterative Methods for Solving Fuzzy Volterra-Fredholm Integral Equations

Cited by 27 publications

References 18 publications

Surprising solutions for some challenging problems arising from boundary layer theory by a new technique: the homotopy contraction mapping technique (HCMT)

Surprising solutions for some challenging problems arising from boundary layer theory by a new technique: the homotopy contraction mapping technique (HCMT)

Optimal Solution of Fuzzy Transshipment Problem Using Generalized Hexagonal Fuzzy Numbers

Laplace discrete decomposition method for solving nonlinear Volterra-Fredholm integro-differential equations

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