Direct regularization for system of integral-algebraic equations of index-1

Farahani, M. S.; Hadizadeh, M.

doi:10.1080/17415977.2017.1347169

Cited by 17 publications

(4 citation statements)

References 22 publications

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“…Further issues related to applications and theoretical analysis of the Lavrentiev‐iterated method for Volterra integral equations and IAEs of index 1 with monotone operators can be found in the studies of Plato and Farahani and Hadizadeh and references therein.…”

Section: Two Families Of Iterative Regularization Methodsmentioning

confidence: 99%

Adaptive iterative regularization schemes for two‐dimensional integral‐algebraic systems

Farahani

Hadizadeh

Bulatov

et al. 2019

Math Methods in App Sciences

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The main idea of this paper is to utilize the adaptive iterative schemes based on regularization techniques for moderately ill-posed problems that are obtained by a system of linear two-dimensional Volterra integral equations with a singular matrix in the leading part. These problems may arise in the modeling of certain heat conduction processes as well as in the dynamic simulation packages such as compressible flow through a plant piping network. Owing to the ill-posed nature of the first kind Volterra equation that appears in the system, we will focus on the two families of regularization algorithms, ie, the Landweber and Lavrentiev type methods, where we treat both the exact and perturbed data. Our aim is to work directly with the original Volterra equations without any kind of reduction. Two fast iterative algorithms with reasonable computational complexity are developed. Numerical experiments on a few test problems are used to illustrate the validity and efficiency of the proposed iterative methods in comparison with the classical regularization methods.

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Section: Two Families Of Iterative Regularization Methodsmentioning

confidence: 99%

Adaptive iterative regularization schemes for two‐dimensional integral‐algebraic systems

Farahani

Hadizadeh

Bulatov

et al. 2019

Math Methods in App Sciences

View full text Add to dashboard Cite

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“…Several researchers have adopted different techniques for solving system of integral algebraic equations [2,5,8,21,24,28]. Our suggestion is by employing of Bernstein polynomials and combining with some other concepts to obtain a numerical solution for (1.1).…”

Section: Theorem 1 ([2]mentioning

confidence: 99%

“…In this example Table 1 shows absolute errors for n = 8 and n = 11 by using the present method at selected points. In Table 2, we compare the maximum absolute error for the present method at n = 11 with method [21] and method [8]. Figure 1 with the exact solution y(t) = e t and z(t) = e −t .…”

Section: Volterra Integral-algebraic Equations 647mentioning

confidence: 99%

A numerical solution of Volterra integral-algebraic equations using Bernstein polynomials

Enteghami-Orimi¹,

Babakhani²,

Hosainzadeh³

2021

MMN

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The principal aim of this paper is to serve the numerical solution for a linear integralalgebraic equation (IAE) by using Bernstein polynomials. Employing of Bernstein polynomials, the system of integral equations is approximated by the Gaussian quadrature formula with respect to the Legendre weight function. The proposed method reduces the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical method. Moreover, the convergence analysis of this algorithm will be shown by preparing some theorems. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods.

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“…Since then, lots of researchers focus on numerical methods of IAEs. In particular, in Hadizadeh et al (2011), spectral methods are used to solve the system of IAEs; in Ghoreishi et al (2012) and Pishbin (2015), polynomial spline collocation methods are applied to semi-explicit index-2 and index-3 IAEs, respectively; in Brunner (2013, 2016), collocation methods are employed to approximate the solution of general linear IAEs of index 1 and index 2; in Shiri (2014), higher index nonlinear IAEs of Hessenberg type are solved by discontinuous collocation methods; Legendre collocation methods are studied in Pishbin et al (2011); block-pulse functions' direct methods are investigated in Balakumar and Murugesan (2015); a direct regularization method is applied to IAEs of index 1 in Farahani and Hadizadeh (2018); in Sohrabi and Ranjbar (2019), Sinc-collocation discretization is used to IAEs of index 1.…”

mentioning

confidence: 99%

On the convergence of multistep collocation methods for integral-algebraic equations of index 1

2020

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The multistep collocation method is introduced to solve integral-algebraic equations of index 1. The existence and uniqueness of the multistep collocation solution are proved. The convergence of the perturbed multistep collocation method is also investigated, which extends and includes the analysis of the multistep collocation method without perturbed terms. Some numerical experiments are given to illustrate the theoretical results. Keywords Integral-algebraic equations • Index 1 • Multistep collocation method • Existence and uniqueness • Convergence Mathematics Subject Classification 65R20 1 Introduction Volterra integral equations (VIEs) have rich applications in physics, biology, chemistry, etc. Generally, VIEs are divided into two classes: first-kind VIEs and second-kind VIEs. For first-kind VIEs, the unknown function only appears inside the integral, but for second-kind Communicated by Antonio José Silva Neto.

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Direct regularization for system of integral-algebraic equations of index-1

Cited by 17 publications

References 22 publications

Adaptive iterative regularization schemes for two‐dimensional integral‐algebraic systems

Adaptive iterative regularization schemes for two‐dimensional integral‐algebraic systems

A numerical solution of Volterra integral-algebraic equations using Bernstein polynomials

On the convergence of multistep collocation methods for integral-algebraic equations of index 1

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