A spectral collocation matrix method for solving linear Fredholm integro-differential–difference equations

Öztürk, Yalçın; Demir, Atılım Ilker

doi:10.1007/s40314-021-01610-7

Cited by 3 publications

(1 citation statement)

References 30 publications

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“…Furthermore, in [31], the nonlinear fractional pantograph equation was handled through the employment of Chebyshev polynomials of the third kind. For additional contributions relating to Chebyshev polynomials, see, for instance, [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Numerical Contrivance for Kawahara-Type Differential Equations Based on Fifth-Kind Chebyshev Polynomials

et al. 2023

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This article proposes a numerical algorithm utilizing the spectral Tau method for numerically handling the Kawahara partial differential equation. The double basis of the fifth-kind Chebyshev polynomials and their shifted ones are used as basis functions. Some theoretical results of the fifth-kind Chebyshev polynomials and their shifted ones are used in deriving our proposed numerical algorithm. The nonlinear term in the equation is linearized using a new product formula of the fifth-kind Chebyshev polynomials with their first derivative polynomials. Some illustrative examples are presented to ensure the applicability and efficiency of the proposed algorithm. Furthermore, our proposed algorithm is compared with other methods in the literature. The presented numerical method results ensure the accuracy and applicability of the presented algorithm.

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Section: Introductionmentioning

confidence: 99%

Numerical Contrivance for Kawahara-Type Differential Equations Based on Fifth-Kind Chebyshev Polynomials

et al. 2023

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New Operational Matrices of Dejdumrong Polynomials to Solve Linear Fredholm-Volterra-Type Functional Integral Equations

Kherd

Karim

Husain

2022

Studies in Systems, Decision and Control

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A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials

et al. 2023

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The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which is based on the spectral tau method. There are two sets of basis functions used. The first set is the set of non-symmetric polynomials, namely, the shifted Chebyshev polynomials of the sixth-kind (CPs6), and the second set is a set of modified shifted CPs6. The approximation of the solution is written as a product of the two chosen basis function sets. For this method, the key concept is to transform the problem governed by the underlying conditions into a set of linear algebraic equations that can be solved by means of an appropriate numerical scheme. The error analysis of the proposed extension is also thoroughly investigated. Finally, a number of examples are shown to illustrate the reliability and accuracy of the suggested tau method.

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A spectral collocation matrix method for solving linear Fredholm integro-differential–difference equations

Cited by 3 publications

References 30 publications

Numerical Contrivance for Kawahara-Type Differential Equations Based on Fifth-Kind Chebyshev Polynomials

Numerical Contrivance for Kawahara-Type Differential Equations Based on Fifth-Kind Chebyshev Polynomials

New Operational Matrices of Dejdumrong Polynomials to Solve Linear Fredholm-Volterra-Type Functional Integral Equations

A Tau Approach for Solving Time-Fractional Heat Equation Based on the Shifted Sixth-Kind Chebyshev Polynomials

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