The Uniform Convergence of a DG Method for a Singularly Perturbed Volterra Integro-Differential Equation

Tao, X.; Xie, Zhongliang

doi:10.1007/s10473-023-0514-8

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2023

2024

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Cited by 2 publications

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“…Their results' proofs are founded on the Banach fixed-point theorem and the Leray-Schau alternative. The objective of [17] is to establish a discontinuous Galerkin method with a one-sided flux for a singularly perturbed regular Volterra integrodifferential equation. In [18], the authors proposed adequate requirements for the estimated controllability of a class of fractional differential systems in Banach space with a fixed delay.…”

Section: Introductionmentioning

confidence: 99%

A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations

Moumen,

Mennouni,

Bouye

2023

Mathematics

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In this paper, a new approach for numerically solving the system of fractional integrodifferential equations is devised. To approximate the issue, we employ Vieta–Fibonacci polynomials as basis functions and derive the projection method for Caputo fractional order for the first time. An efficient transformation reduces the problem to a system of two independent equations. Solving two algebraic equations yields an approximate solution to the problem. The proposed method’s efficiency and accuracy are validated. We demonstrate the existence of the solution to the approximate problem and conduct an error analysis. Numerical tests reinforce the interpretations of the theory.

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Section: Introductionmentioning

confidence: 99%