On the weakly singular integro-differential nonlinear Volterra equation depending in acceleration term

Mourad Ghiat; Hamza Guebbai; Muhammet Kurulay; Sami Segni

doi:10.1007/s40314-020-01235-2

On the weakly singular integro-differential nonlinear Volterra equation depending in acceleration term

Mourad Ghiat
, Hamza Guebbai^*
, Muhammet Kurulay
, Sami Segni

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

In this article, our study deals with the existence and the uniqueness of the solution of a second degree integro-differential nonlinear Volterra equation with a weakly singular kernel, i.e., the solution depends on its speed (first derivative) and its acceleration (second derivative); whereas using Nyström method and product integration method with piecewise projection, we approximate this solution.

Original language	English
Article number	206
Journal	Computational and Applied Mathematics
Volume	39
Issue number	3
DOIs	https://doi.org/10.1007/s40314-020-01235-2
Publication status	Published - 1 Sept 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.

Keywords

Fixed point
Integro-differential
Nonlinear equation
Product integration method
Volterra equation

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10.1007/s40314-020-01235-2

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abstract = "In this article, our study deals with the existence and the uniqueness of the solution of a second degree integro-differential nonlinear Volterra equation with a weakly singular kernel, i.e., the solution depends on its speed (first derivative) and its acceleration (second derivative); whereas using Nystr{\"o}m method and product integration method with piecewise projection, we approximate this solution.",

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AU - Kurulay, Muhammet

AU - Segni, Sami

PY - 2020/9/1

Y1 - 2020/9/1

N2 - In this article, our study deals with the existence and the uniqueness of the solution of a second degree integro-differential nonlinear Volterra equation with a weakly singular kernel, i.e., the solution depends on its speed (first derivative) and its acceleration (second derivative); whereas using Nyström method and product integration method with piecewise projection, we approximate this solution.

AB - In this article, our study deals with the existence and the uniqueness of the solution of a second degree integro-differential nonlinear Volterra equation with a weakly singular kernel, i.e., the solution depends on its speed (first derivative) and its acceleration (second derivative); whereas using Nyström method and product integration method with piecewise projection, we approximate this solution.

KW - Fixed point

KW - Integro-differential

KW - Nonlinear equation

KW - Product integration method

KW - Volterra equation

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ER -

On the weakly singular integro-differential nonlinear Volterra equation depending in acceleration term

Abstract

Bibliographical note

Keywords

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