Approximate solution to Fredholm integral equations using linear regression and applications to heat and mass transfer

Ioannou, Yiannos; Fyrillas, Marios M.; Doumanidis, Charalabos C.

doi:10.1016/j.enganabound.2012.02.006

Cited by 17 publications

(8 citation statements)

References 28 publications

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“…Diverse problems in biology and mechanics arise in an integrated one and a multidimensional equation [7][8][9][10] . These equations also appear in mass and heat transfer, fluid mechanics, molecular physics and in many other problems [11][12][13][14][15][16] .…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

Hameed

Al-Saedi

2021

Baghdad Sci.J

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In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R 3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

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Section: Introductionmentioning

confidence: 99%

Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

Hameed

Al-Saedi

2021

Baghdad Sci.J

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“…Functional, delay, difference and neutral integro-differential equations (IDEs) are of great importance especially in the applied sciences, such as mathematics, biology, physics, engineering, electrodynamics, electromagnetics, viscoelasticity, heat and mass transfer (Kürkçü et al 2016(Kürkçü et al , 2017a(Kürkçü et al , b, 2018Yüzbaşı et al 2013;Akyüz-Daşcıoglu 2006;Gülsu et al 2010;Babolian et al 2008;Wang andWang 2013, 2014;Adomian 1994;He 1999He , 2000Wang et al 2016Wang et al , 2017aWang et al , b, c, d, 2008Wang 2018;Liu and Wu 2017;Biazar et al 2011;Reutskiy 2016;Vlasov et al 2015;Dehghan and Shakeri 2008;Heydari et al 2013;Ioannou et al 2012). Most of these equations come to exist when real-life problems are encountered.…”

Section: Introductionmentioning

confidence: 99%

An inventive numerical method for solving the most general form of integro-differential equations with functional delays and characteristic behavior of orthoexponential residual function

2019

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In this study, we constitute the most general form of functional integro-differential equations with functional delays. An inventive method based on Dickson polynomials with the parameter-α along with collocation points is employed to solve them. The stability of the solutions is simulated according to an interval of the parameter-α. A useful computer program is developed to obtain the precise values from the method. The residual error analysis is used to improve the obtained solutions. The characteristic behavior of the residual function is established with the aid of the orthoexponential polynomials. We compare the present numerical results of the method with those obtained by the existing methods in tables. Keywords Collocation points • Dickson and orthoexponential polynomials • Error analysis • Matrix method Mathematical Subject Classification 34K06 • 45J05 • 65L60 • 65R20 Communicated by Hui Liang.

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“…As we have mentioned earlier, the partial differential equation governing the heat transfer process appears as a constraint in the optimization problem (inverse problem). Hence, unlike direct heat transfer problems where only a single solution of the PDE is necessary [26,27,28], in inverse problems each iteration requires the solution of the PDE at least as many times as the number of the optimization variables. In addition, accuracy is very significant due to the sensitivity of the solution on the parameters of the optimization.…”

Section: Introductionmentioning

confidence: 99%

Shape optimization of conductive-media interfaces using an IGA-BEM solver

Κώστας

Fyrillas

Politis

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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In this paper, we present a method that combines the Boundary Element Method (BEM) with IsoGeometric Analysis (IGA) for numerically solving the system of Boundary Integral Equations (BIE) arising in the context of a 2-D steady-state heat conduction problem across a periodic interface separating two conducting and conforming media. Our approach leads to a fast converging solver that achieves the same level of accuracy for fewer degrees of freedom, when compared with low-order BEM. Additionally, an optimization procedure is developed and test cases of interface's shape optimization, with the aim of heat transfer maximization under given constraints, are demonstrated.

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Approximate solution to Fredholm integral equations using linear regression and applications to heat and mass transfer

Cited by 17 publications

References 28 publications

Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

An inventive numerical method for solving the most general form of integro-differential equations with functional delays and characteristic behavior of orthoexponential residual function

Shape optimization of conductive-media interfaces using an IGA-BEM solver

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