Chelyshkov collocation approach for solving linear weakly singular Volterra integral equations

Talaei, Younes

doi:10.1007/s12190-018-1209-5

Cited by 21 publications

(10 citation statements)

References 22 publications

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“…The Chelyshkov basis polynomials given by equation (2.9) can be written in the matrix form [16,25] C…”

Section: Chelyshkov Functionsmentioning

confidence: 99%

“…As already mentioned, the model problem (1.1)-(1.2) is known to possess no exact solutions in general. In this manuscript, we will propose approximation methods as extension of the previous works [17], [11,12], [27], [14], and [25] for solving (1.1)-(1.2). We use the fractional-order polynomials including the Chebyshev, Chelyshkov, and Legendre functions to approximate the solution of (1.1) accurately on the interval [0, R].…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Various Fractional Basis Functions for Solving Fractional-Order Logistic Population Model

Izadi

2021

FU Math Inform

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Three types of orthogonal polynomials (Chebyshev, Chelyshkov, and Legendre) are employed as basis functions in a collocation scheme to solve a nonlinear cubic initial value problem arising in population growth models. The method reduces the given problem to a set of algebraic equations consist of polynomial coefficients. Our main goal is to present a comparative study of these polynomials and to asses their performances and accuracies applied to the logistic population equation. Numerical applications are given to demonstrate the validity and applicability of the method. Comparisons are also made between the present method based on different basis functions and other existing approximation algorithms.

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“…The Chelyshkov basis polynomials given by equation (2.9) can be written in the matrix form [16,25] C…”

Section: Chelyshkov Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison of Various Fractional Basis Functions for Solving Fractional-Order Logistic Population Model

Izadi

2021

FU Math Inform

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“…There are three well-known versions used as popular techniques to determine the expansion coefficients, namely collocation, tau, and Galerkin methods. Classical orthogonal polynomials are used successfully and extensively for the numerical solution of differential equations in spectral methods (see [6][7][8][9][10][11][12][13][14][15][16][17][18]).…”

Section: Introductionmentioning

confidence: 99%

A Finite Difference-Spectral Method for Solving the European Call Option Black–Scholes Equation

Talaei¹,

Hosseinzadeh²,

Noeiaghdam³

2021

MMEP

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In this paper, we present a novel technique based on backward-difference method and Galerkin spectral method for solving Black–Scholes equation. The main propose of this method is to reduce the solution of this problem to the solution of a system of algebraic equations. The convergence order of the proposed method is investigated. Also, we provide numerical experiment to show the validity of proposed method.

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“…Furthermore, the operational matrix of fractional derivatives based on Chelyshkov polynomials for solving multi-order fractional differential equations has been presented in [31] and the operational matrix of fractional integration to solve a class of nonlinear fractional differential equations has been introduced in [32]. Recently, Talaei [33] has proposed a numerical algorithm based on FCHFs for solving linear weakly singular Volterra integral equation.…”

Section: Introductionmentioning

confidence: 99%

An Integral Operational Matrix of Fractional-Order Chelyshkov Functions and Its Applications

2020

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Fractional differential equations have been applied to model physical and engineering processes in many fields of science and engineering. This paper adopts the fractional-order Chelyshkov functions (FCHFs) for solving the fractional differential equations. The operational matrices of fractional integral and product for FCHFs are derived. These matrices, together with the spectral collocation method, are used to reduce the fractional differential equation into a system of algebraic equations. The error estimation of the presented method is also studied. Furthermore, numerical examples and comparison with existing results are given to demonstrate the accuracy and applicability of the presented method.

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Chelyshkov collocation approach for solving linear weakly singular Volterra integral equations

Cited by 21 publications

References 22 publications

Comparison of Various Fractional Basis Functions for Solving Fractional-Order Logistic Population Model

Comparison of Various Fractional Basis Functions for Solving Fractional-Order Logistic Population Model

A Finite Difference-Spectral Method for Solving the European Call Option Black–Scholes Equation

An Integral Operational Matrix of Fractional-Order Chelyshkov Functions and Its Applications

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