Generalized mapped nodal Laguerre spectral collocation method for Volterra delay integro-differential equations with noncompact kernels

Tang, Zhuyan; Tohidi, Emran; He, Fuli

doi:10.1007/s40314-020-01352-y

Cited by 12 publications

(2 citation statements)

References 21 publications

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“…Tang et al. ( 2020 ) constructed a numerical scheme based on the method of Laguerre spectral collocation for Volterra delay integro-differential equations with non-compact kernels.…”

Section: Introductionmentioning

confidence: 99%

An optimization method for studying fractional-order tuberculosis disease model via generalized Laguerre polynomials

et al. 2023

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Tuberculosis (TB) is a deadly contagious disease that affects vital organs of the body, especially the lungs. Although the disease is preventable, there are still concerns about its continued spread. Without effective prevention or appropriate treatment, TB infection can be fatal to humans. This paper presents a fractional-order TB disease (FTBD) model to analyze TB dynamics and a new optimization method to solve it. The method is based on the basis functions of generalized Laguerre polynomials (GLPs) and some new operational matrices of derivatives in the Caputo sense. Finding the optimal solution to the FTBD model is reduced to solving a system of nonlinear algebraic equations with the aid of GLPs using the Lagrange multipliers method. A numerical simulation is also carried out to determine the impact of the presented method on the susceptible, exposed, infected without treatment, infected with treatment, and recovered cases in the population.

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“…Tang et al. ( 2020 ) constructed a numerical scheme based on the method of Laguerre spectral collocation for Volterra delay integro-differential equations with non-compact kernels.…”

Section: Introductionmentioning

confidence: 99%

An optimization method for studying fractional-order tuberculosis disease model via generalized Laguerre polynomials

et al. 2023

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“…Different Volterra integral equations are handled by Bernstein polynomials, block pulse functions, least squares method, Haar wavelets, Walsh functions, Chebyshev and Legendre polynomials, and other functions. We only mentioned the referenced such as [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and other relevant literatures. On the other hand, some authors obtained the numerical solution of stochastic Volterra integral equation by Euler-Maruyama approximation or iterative algorithm, for example [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Multidimensional Stochastic Itô-Volterra Integral Equation Based on the Least Squares Method and Block Pulse Function

Jiang

Deng

2021

Mathematical Problems in Engineering

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In this paper, a method based on the least squares method and block pulse function is proposed to solve the multidimensional stochastic Itô-Volterra integral equation. The Itô-Volterra integral equation is transformed into a linear algebraic equation. Furthermore, the error analysis is given by the isometry property and Doob’s inequality. Numerical examples verify the effectiveness and precision of this method.

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A Study of the Fractional Tumour–Immune Unhealthy Diet Model Using the Pseudo-operational Matrix Method

Kumar,

Gupta

2023

Studies in Computational Intelligence

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Generalized mapped nodal Laguerre spectral collocation method for Volterra delay integro-differential equations with noncompact kernels

Cited by 12 publications

References 21 publications

An optimization method for studying fractional-order tuberculosis disease model via generalized Laguerre polynomials

An optimization method for studying fractional-order tuberculosis disease model via generalized Laguerre polynomials

Numerical Solution of Multidimensional Stochastic Itô-Volterra Integral Equation Based on the Least Squares Method and Block Pulse Function

A Study of the Fractional Tumour–Immune Unhealthy Diet Model Using the Pseudo-operational Matrix Method

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