Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method

Runge-Kutta-Nyström (RKN) method is adapted for solving the special second order delay differential equations (DDEs). The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical problems in engineering 2013-01, Vol.2013 (2013), p.1-7
Main Authors: Siri, Z., Senu, Norazak, Ismail, F., Mechee, M.
Format: Article
Language:English
Subjects:
Applied mathematics
Delay
Differential equations
Engineering
Mathematical analysis
Mathematical problems
Methods
Neural networks
Numerical analysis
Ordinary differential equations
Runge-Kutta method
Studies
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c356t-29046fc33d8360ad977db6fca738e070ff7b8fa57ad22de8c739d2a84326a1153
cites cdi_FETCH-LOGICAL-c356t-29046fc33d8360ad977db6fca738e070ff7b8fa57ad22de8c739d2a84326a1153
container_end_page 7
container_issue 2013
container_start_page 1
container_title Mathematical problems in engineering
container_volume 2013
creator Siri, Z.
Senu, Norazak
Ismail, F.
Mechee, M.
description Runge-Kutta-Nyström (RKN) method is adapted for solving the special second order delay differential equations (DDEs). The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK) method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement.
doi_str_mv 10.1155/2013/830317
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1944192463</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1944192463</sourcerecordid><originalsourceid>FETCH-LOGICAL-c356t-29046fc33d8360ad977db6fca738e070ff7b8fa57ad22de8c739d2a84326a1153</originalsourceid><addsrcrecordid>eNqF0E1PwyAYB3BiNHFOT94NiTdNHS9toUezzZc4XeJc4q1hBTaWrt2AavrF_AJ-MVnqwZsnnsAPnoc_AOcY3WCcJAOCMB1wiihmB6CHk5RGCY7ZYagRiSNM6PsxOHFujRDBCeY9IEfGqsKXLZzV5YeplnC2VYURJZypoq4knFqpLBypUrRwZLRWVlV-fz7eNcKbunJw7vb3XptqqaKnxnsRvbTO2--vDXxWflXLU3CkRenU2e_aB_O78dvwIZpM7x-Ht5OooEnqI5KhONUFpZLTFAmZMSYXYUMwyhViSGu24FokTEhCpOIFo5kkgseUpCL8n_bBZffu1ta7Rjmfr-vGVqFljrM4xhmJUxrUdacKWztnlc631myEbXOM8n2M-T7GvIsx6KtOr0wlxaf5B190WAWitPiDMeJh0B_E0Hw1</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1944192463</pqid></control><display><type>article</type><title>Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method</title><source>Wiley_OA刊</source><source>Publicly Available Content (ProQuest)</source><source>IngentaConnect Journals</source><creator>Siri, Z. ; Senu, Norazak ; Ismail, F. ; Mechee, M.</creator><contributor>Yi, Yang</contributor><creatorcontrib>Siri, Z. ; Senu, Norazak ; Ismail, F. ; Mechee, M. ; Yi, Yang</creatorcontrib><description>Runge-Kutta-Nyström (RKN) method is adapted for solving the special second order delay differential equations (DDEs). The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK) method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2013/830317</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Applied mathematics ; Delay ; Differential equations ; Engineering ; Mathematical analysis ; Mathematical problems ; Methods ; Neural networks ; Numerical analysis ; Ordinary differential equations ; Runge-Kutta method ; Studies</subject><ispartof>Mathematical problems in engineering, 2013-01, Vol.2013 (2013), p.1-7</ispartof><rights>Copyright © 2013 M. Mechee et al.</rights><rights>Copyright © 2013 M. Mechee et al.; This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c356t-29046fc33d8360ad977db6fca738e070ff7b8fa57ad22de8c739d2a84326a1153</citedby><cites>FETCH-LOGICAL-c356t-29046fc33d8360ad977db6fca738e070ff7b8fa57ad22de8c739d2a84326a1153</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/1944192463/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/1944192463?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25751,27922,27923,37010,44588,74896</link.rule.ids></links><search><contributor>Yi, Yang</contributor><creatorcontrib>Siri, Z.</creatorcontrib><creatorcontrib>Senu, Norazak</creatorcontrib><creatorcontrib>Ismail, F.</creatorcontrib><creatorcontrib>Mechee, M.</creatorcontrib><title>Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method</title><title>Mathematical problems in engineering</title><description>Runge-Kutta-Nyström (RKN) method is adapted for solving the special second order delay differential equations (DDEs). The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK) method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement.</description><subject>Applied mathematics</subject><subject>Delay</subject><subject>Differential equations</subject><subject>Engineering</subject><subject>Mathematical analysis</subject><subject>Mathematical problems</subject><subject>Methods</subject><subject>Neural networks</subject><subject>Numerical analysis</subject><subject>Ordinary differential equations</subject><subject>Runge-Kutta method</subject><subject>Studies</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqF0E1PwyAYB3BiNHFOT94NiTdNHS9toUezzZc4XeJc4q1hBTaWrt2AavrF_AJ-MVnqwZsnnsAPnoc_AOcY3WCcJAOCMB1wiihmB6CHk5RGCY7ZYagRiSNM6PsxOHFujRDBCeY9IEfGqsKXLZzV5YeplnC2VYURJZypoq4knFqpLBypUrRwZLRWVlV-fz7eNcKbunJw7vb3XptqqaKnxnsRvbTO2--vDXxWflXLU3CkRenU2e_aB_O78dvwIZpM7x-Ht5OooEnqI5KhONUFpZLTFAmZMSYXYUMwyhViSGu24FokTEhCpOIFo5kkgseUpCL8n_bBZffu1ta7Rjmfr-vGVqFljrM4xhmJUxrUdacKWztnlc631myEbXOM8n2M-T7GvIsx6KtOr0wlxaf5B190WAWitPiDMeJh0B_E0Hw1</recordid><startdate>20130101</startdate><enddate>20130101</enddate><creator>Siri, Z.</creator><creator>Senu, Norazak</creator><creator>Ismail, F.</creator><creator>Mechee, M.</creator><general>Hindawi Publishing Corporation</general><general>Hindawi Limited</general><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20130101</creationdate><title>Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method</title><author>Siri, Z. ; Senu, Norazak ; Ismail, F. ; Mechee, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c356t-29046fc33d8360ad977db6fca738e070ff7b8fa57ad22de8c739d2a84326a1153</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Applied mathematics</topic><topic>Delay</topic><topic>Differential equations</topic><topic>Engineering</topic><topic>Mathematical analysis</topic><topic>Mathematical problems</topic><topic>Methods</topic><topic>Neural networks</topic><topic>Numerical analysis</topic><topic>Ordinary differential equations</topic><topic>Runge-Kutta method</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Siri, Z.</creatorcontrib><creatorcontrib>Senu, Norazak</creatorcontrib><creatorcontrib>Ismail, F.</creatorcontrib><creatorcontrib>Mechee, M.</creatorcontrib><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access Journals</collection><collection>CrossRef</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Database‎ (1962 - current)</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East &amp; Africa Database</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies &amp; Aerospace Database</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Mathematical problems in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Siri, Z.</au><au>Senu, Norazak</au><au>Ismail, F.</au><au>Mechee, M.</au><au>Yi, Yang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2013-01-01</date><risdate>2013</risdate><volume>2013</volume><issue>2013</issue><spage>1</spage><epage>7</epage><pages>1-7</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>Runge-Kutta-Nyström (RKN) method is adapted for solving the special second order delay differential equations (DDEs). The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK) method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Publishing Corporation</pub><doi>10.1155/2013/830317</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1024-123X
ispartof Mathematical problems in engineering, 2013-01, Vol.2013 (2013), p.1-7
issn 1024-123X
1563-5147
language eng
recordid cdi_proquest_journals_1944192463
source Wiley_OA刊; Publicly Available Content (ProQuest); IngentaConnect Journals
subjects Applied mathematics
Delay
Differential equations
Engineering
Mathematical analysis
Mathematical problems
Methods
Neural networks
Numerical analysis
Ordinary differential equations
Runge-Kutta method
Studies
title Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T13%3A15%3A58IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Directly%20Solving%20Special%20Second%20Order%20Delay%20Differential%20Equations%20Using%20Runge-Kutta-Nystr%C3%B6m%20Method&rft.jtitle=Mathematical%20problems%20in%20engineering&rft.au=Siri,%20Z.&rft.date=2013-01-01&rft.volume=2013&rft.issue=2013&rft.spage=1&rft.epage=7&rft.pages=1-7&rft.issn=1024-123X&rft.eissn=1563-5147&rft_id=info:doi/10.1155/2013/830317&rft_dat=%3Cproquest_cross%3E1944192463%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c356t-29046fc33d8360ad977db6fca738e070ff7b8fa57ad22de8c739d2a84326a1153%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1944192463&rft_id=info:pmid/&rfr_iscdi=true