Legendre spectral-collocation method for Volterra integral equations with non-vanishing delay

Gu, Zhi‐Gang; Chen, Yanping

doi:10.1007/s10092-013-0083-7

Cited by 13 publications

(2 citation statements)

References 21 publications

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“…Wan, Chen and Huang [21] used the spectral Galerkin method to solve the nonlinear Volterra integral equations of the second kind. The authors in [1,9,10,19,22,23,26,31] proposed the spectral Legendre-collocation method for Volterra integral or integro-differential equations with smooth kernels. In [6-8, 12, 24, 25, 29, 30, 32] the spectral Jacobi-collocation method was successfully applied to solve Volterra integral or integro-differential equations with weakly kernels and fractional integro-differential equations.…”

Section: Introductionmentioning

confidence: 99%

Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels

Shi

Chen

2016

Adv. Appl. Math. Mech.

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A spectral Jacobi-collocation approximation is proposed for Volterra delay integro-differential equations with weakly singular kernels. In this paper, we consider the special case that the underlying solutions of equations are sufficiently smooth. We provide a rigorous error analysis for the proposed method, which shows that both the errors of approximate solutions and the errors of approximate derivatives decay exponentially in L ∞ norm and weighted L 2 norm. Finally, two numerical examples are presented to demonstrate our error analysis.

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Section: Introductionmentioning

confidence: 99%

Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels

Shi

Chen

2016

Adv. Appl. Math. Mech.

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“…2006; Bhrawy and Alofi 2013; Gu and Chen 2014; Bhrawy and Abdelkawy 2015; Bhrawy 2016a) is a specific type of spectral methods, that is more applicable and widely used to solve almost types of differential (Bhrawy et al. 2016b; Tatari and Haghighi 2014), integral (Bhrawy et al.…”

Section: Introductionmentioning

confidence: 99%

A space–time spectral collocation algorithm for the variable order fractional wave equation

et al. 2016

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The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space–time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order fractional derivative is described in the Caputo sense. The proposed method is a combination of shifted Jacobi–Gauss–Lobatto collocation scheme for the spatial discretization and the shifted Jacobi–Gauss–Radau collocation scheme for temporal discretization. The aforementioned problem is then reduced to a problem consists of a system of easily solvable algebraic equations. Finally, numerical examples are presented to show the effectiveness of the proposed numerical method.

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Piecewise spectral collocation method for system of Volterra integral equations

2016

Adv Comput Math

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Legendre spectral-collocation method for Volterra integral equations with non-vanishing delay

Cited by 13 publications

References 21 publications

Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels

Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels

A space–time spectral collocation algorithm for the variable order fractional wave equation

Piecewise spectral collocation method for system of Volterra integral equations

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