Fifth order multistep block method for solving volterra integro-differential equations of second kind

In the present paper, the multistep block method is proposed to solve the linear and non-linear Volterra integro-differential equations (VIDEs) of the second kind using constant step size. The proposed block method of order five consists of two point block method presented as in the simple form of A...

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Main Authors:	Zanariah Abdul Majid, Nurul Atikah Mohamed
Format:	Article
Language:	English
Published:	Penerbit Universiti Kebangsaan Malaysia 2019
Online Access:	http://journalarticle.ukm.my/13328/ http://journalarticle.ukm.my/13328/ http://journalarticle.ukm.my/13328/1/22%20Zanariah%20Abdul%20Majid.pdf

id	ukm-13328
recordtype	eprints
spelling	ukm-133282019-08-29T21:45:12Z http://journalarticle.ukm.my/13328/ Fifth order multistep block method for solving volterra integro-differential equations of second kind Zanariah Abdul Majid, Nurul Atikah Mohamed, In the present paper, the multistep block method is proposed to solve the linear and non-linear Volterra integro-differential equations (VIDEs) of the second kind using constant step size. The proposed block method of order five consists of two point block method presented as in the simple form of Adams Moulton type. The numerical solutions are obtained at two new values simultaneously at each of the integration step. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The approximation of the integral part is estimated using the Boole’s quadrature rule. The stability region is shown, and the numerical results are presented to illustrate the performance of the proposed method in terms of accuracy, total function calls and execution times compared to the existing method. Penerbit Universiti Kebangsaan Malaysia 2019-03 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/13328/1/22%20Zanariah%20Abdul%20Majid.pdf Zanariah Abdul Majid, and Nurul Atikah Mohamed, (2019) Fifth order multistep block method for solving volterra integro-differential equations of second kind. Sains Malaysiana, 48 (3). pp. 677-684. ISSN 0126-6039 http://www.ukm.my/jsm/malay_journals/jilid48bil3_2019/KandunganJilid48Bil3_2019.html
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	In the present paper, the multistep block method is proposed to solve the linear and non-linear Volterra integro-differential equations (VIDEs) of the second kind using constant step size. The proposed block method of order five consists of two point block method presented as in the simple form of Adams Moulton type. The numerical solutions are obtained at two new values simultaneously at each of the integration step. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The approximation of the integral part is estimated using the Boole’s quadrature rule. The stability region is shown, and the numerical results are presented to illustrate the performance of the proposed method in terms of accuracy, total function calls and execution times compared to the existing method.
format	Article
author	Zanariah Abdul Majid, Nurul Atikah Mohamed,
spellingShingle	Zanariah Abdul Majid, Nurul Atikah Mohamed, Fifth order multistep block method for solving volterra integro-differential equations of second kind
author_facet	Zanariah Abdul Majid, Nurul Atikah Mohamed,
author_sort	Zanariah Abdul Majid,
title	Fifth order multistep block method for solving volterra integro-differential equations of second kind
title_short	Fifth order multistep block method for solving volterra integro-differential equations of second kind
title_full	Fifth order multistep block method for solving volterra integro-differential equations of second kind
title_fullStr	Fifth order multistep block method for solving volterra integro-differential equations of second kind
title_full_unstemmed	Fifth order multistep block method for solving volterra integro-differential equations of second kind
title_sort	fifth order multistep block method for solving volterra integro-differential equations of second kind
publisher	Penerbit Universiti Kebangsaan Malaysia
publishDate	2019
url	http://journalarticle.ukm.my/13328/ http://journalarticle.ukm.my/13328/ http://journalarticle.ukm.my/13328/1/22%20Zanariah%20Abdul%20Majid.pdf
first_indexed	2023-09-18T20:04:36Z
last_indexed	2023-09-18T20:04:36Z
_version_	1777407074635874304

Fifth order multistep block method for solving volterra integro-differential equations of second kind

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