An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition

In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in th...

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Detalles Bibliográficos
Autores principales: Durmaz, Muhammet Enes, Amirali, Ilhame, Amiraliyev, Gabil M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Original Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9178336/
https://www.ncbi.nlm.nih.gov/pubmed/35698573
http://dx.doi.org/10.1007/s12190-022-01757-4
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author Durmaz, Muhammet Enes
Amirali, Ilhame
Amiraliyev, Gabil M.
author_facet Durmaz, Muhammet Enes
Amirali, Ilhame
Amiraliyev, Gabil M.
author_sort Durmaz, Muhammet Enes
collection PubMed
description In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in the initial condition. The proposed technique acquires a uniform second-order convergence in respect to perturbation parameter. Further provided the numerical results to support the theoretical estimates.
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spelling pubmed-91783362022-06-09 An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition Durmaz, Muhammet Enes Amirali, Ilhame Amiraliyev, Gabil M. J Appl Math Comput Original Research In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in the initial condition. The proposed technique acquires a uniform second-order convergence in respect to perturbation parameter. Further provided the numerical results to support the theoretical estimates. Springer Berlin Heidelberg 2022-06-09 2023 /pmc/articles/PMC9178336/ /pubmed/35698573 http://dx.doi.org/10.1007/s12190-022-01757-4 Text en © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2022 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Original Research
Durmaz, Muhammet Enes
Amirali, Ilhame
Amiraliyev, Gabil M.
An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition
title An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition
title_full An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition
title_fullStr An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition
title_full_unstemmed An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition
title_short An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition
title_sort efficient numerical method for a singularly perturbed fredholm integro-differential equation with integral boundary condition
topic Original Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9178336/
https://www.ncbi.nlm.nih.gov/pubmed/35698573
http://dx.doi.org/10.1007/s12190-022-01757-4
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