Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments

Gürbüz, Burcu; Sezer, Mehmet; Güler, Coşkun

doi:10.1155/2014/682398

Cited by 27 publications

(15 citation statements)

References 26 publications

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“…Laguerre polynomials are used to solve some integer order integro-differential equations. These equations are given as Altarelli-Parisi equation (Kobayashi et al 1995), Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation (Schoeffel 1999), Pantograph-type Volterra integrodifferential equation (Yüzbaşı 2014), linear Fredholm integro-differential equation (Baykus Savasaneril & Sezer 2016;Gürbüz et al 2014), linear integro-differential equation (Al-Zubaidy 2013), parabolic-type Volterra partial integro-differential equation (Gürbüz & Sezer 2017a), nonlinear partial integro-differential equation (Gürbüz & Sezer 2017b), delay partial functional differential equation (Gürbüz & Sezer 2017c). Besides, Laguerre polynomials are used to solve the fractional integro-differential equation (Mahdy & Shwayyea 2016).…”

Section: Introductionmentioning

confidence: 99%

Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials

Daşçıoğlu¹,

Bayram²

2019

JSM

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The main purpose of this study was to present an approximation method based on the Laguerre polynomials to obtain the solutions of the fractional linear Fredholm integro-differential equations. This method transforms the integro-differential equation to a system of linear algebraic equations by using the collocation points. In addition, the matrix relation for Caputo fractional derivative of Laguerre polynomials is also obtained. Besides, some examples are presented to illustrate the accuracy of the method and the results are discussed. ABSTRAKTujuan utama kajian ini adalah untuk mengemukakan kaedah penghampiran berdasarkan polinomial Laguerre untuk mendapatkan penyelesaian pecahan linear persamaan pembezaan-kamiran Fredholm. Kaedah ini menjelmakan persamaan pembezaan-kamiran ke sistem persamaan aljabar linear dengan menggunakan titik-titik kolokasi. Di samping itu, hubungan matriks untuk terbitan pecahan Caputo polinomial Laguerre juga diperoleh. Selain itu, beberapa contoh dibentangkan untuk menggambarkan ketepatan kaedah dan hasilnya dibincangkan.Kata kunci: Persamaan pembezaan-kamiran Fredholm; persamaan pembezaan-kamiran pecahan; polinomial Laguerre

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Section: Introductionmentioning

confidence: 99%

Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials

Daşçıoğlu¹,

Bayram²

2019

JSM

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“…However, most of the mentioned type delay equations have not analytical and numerical solutions; therefore, numerical methods are required to obtain approximate solutions. For this purpose, by means of the matrix method based on collocation points which have been given by Sezer and coworkers [2,6,16,17,21,26,29,36], we develop a novel matrix technique to find the approximate solution of Eq. 1 under the initial condition yðaÞ ¼ k in the truncated Morgan-Voyce series form…”

Section: Introductionmentioning

confidence: 99%

A numerical approach for a nonhomogeneous differential equation with variable delays

2018

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In this study, we consider a linear nonhomogeneous differential equation with variable coefficients and variable delays and present a novel matrix-collocation method based on Morgan-Voyce polynomials to obtain the approximate solutions under the initial conditions. The method reduces the equation with variable delays to a matrix equation with unknown MorganVoyce coefficients. Thereby, the solution is obtained in terms of Morgan-Voyce polynomials. In addition, two test problems together with error analysis are performed to illustrate the accuracy and applicability of the method; the obtained results are scrutinized and interpreted by means of tables and figures.

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“…In this paper, by considering the matrix technique based on collocation points, which have been used by Sezer and coworkers [5,6,[8][9][10][11][12][13][14][15][16][17][18][19], we purpose a new numerical technique to find an approximate solution of the problem (1)- (2). The solution is of the form…”

Section: Introductionmentioning

confidence: 99%

A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays

Gümgüm

Savaşaneril

Kürkçü

et al. 2018

Sakarya University Journal of Science

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In this paper, a new numerical matrix-collocation technique is considered to solve functional integrodifferential equations involving variable delays under the initial conditions. This technique is based essentially on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points. Some descriptive examples are performed to observe the practicability of the technique and the residual error analysis is employed to improve the obtained solutions. Also, the numerical results obtained by using these collocation points are compared in tables and figures.

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Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments

Cited by 27 publications

References 26 publications

Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials

Solving Fractional Fredholm Integro-Differential Equations by Laguerre Polynomials

A numerical approach for a nonhomogeneous differential equation with variable delays

A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays

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