Stabilized cubic c1-spline collocation method for solving first-order ordinary initial value problems

This paper is concerned with a construction of a "variable" one-parameter cubic C 1 -spline collocation method for solving the initial value problem (IVP)viz where the collocation point . The presented method will be shown to be strongly unstable if β ≤ 1/2. It turns out that the proposed...

Full description

Saved in:
Bibliographic Details
Published in:International journal of computer mathematics 2000-01, Vol.74 (1), p.87-96
Main Authors: Sallam, S., Naim Anwar, M.
Format: Article
Language:English
Subjects:
A-stability
A-stabilized Simpson's rule
absolute stability
collocation methods
Exact sciences and technology
First order initial value problem
G.1.7
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 96
container_issue 1
container_start_page 87
container_title International journal of computer mathematics
container_volume 74
creator Sallam, S.
Naim Anwar, M.
description This paper is concerned with a construction of a "variable" one-parameter cubic C 1 -spline collocation method for solving the initial value problem (IVP)viz where the collocation point . The presented method will be shown to be strongly unstable if β ≤ 1/2. It turns out that the proposed method is a continuous extension of the A-stabilized version of Simpson's rule introduced in [1], if β = 1. Moreover, the method is of order three, for β ∈ (1/2, 1) and is of order four, if β = 1 and y ∈ C 5 [0,b].
doi_str_mv 10.1080/00207160008804924
format article
fullrecord <record><control><sourceid>pascalfrancis_infor</sourceid><recordid>TN_cdi_pascalfrancis_primary_1386512</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1386512</sourcerecordid><originalsourceid>FETCH-LOGICAL-i1302-78d8fb91e7c776b4540074c41e419c152a7b2545ec1ba30a0be5728768c6744f3</originalsourceid><addsrcrecordid>eNqFkD1PwzAQhi0EEqHwA9g8sAbOjhM7Eguq-JIqMQBzZDsOGDlxZLuF8utJVJg6sNwN9zynuxehcwKXBARcAVDgpAIAIYDVlB2gjACtc6BVeYiyeZ7PwDE6ifFj5mpeZcg8J6mss9-mxXqtrMaa5HF0djBYe-e8lsn6AfcmvfsWdz7g6N3GDm-4syGm3IfWBDxVO8iwxXawyUqHN9KtDR6DV8708RQdddJFc_bbF-j17vZl-ZCvnu4flzer3JICaM5FKzpVE8M155ViJQPgTDNiGKk1KankipasNJooWYAEZUpOBa-ErjhjXbFAF7u9o4xaui7IQdvYjMH203ENKURVEjph1zvMDtNDvfz0wbVNklvnw59TEGjmZJu9ZCed_6vvWU36SsUPmfR-0g</addsrcrecordid><sourcetype>Index Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Stabilized cubic c1-spline collocation method for solving first-order ordinary initial value problems</title><source>Taylor and Francis Science and Technology Collection</source><creator>Sallam, S. ; Naim Anwar, M.</creator><creatorcontrib>Sallam, S. ; Naim Anwar, M.</creatorcontrib><description>This paper is concerned with a construction of a "variable" one-parameter cubic C 1 -spline collocation method for solving the initial value problem (IVP)viz where the collocation point . The presented method will be shown to be strongly unstable if β ≤ 1/2. It turns out that the proposed method is a continuous extension of the A-stabilized version of Simpson's rule introduced in [1], if β = 1. Moreover, the method is of order three, for β ∈ (1/2, 1) and is of order four, if β = 1 and y ∈ C 5 [0,b].</description><identifier>ISSN: 0020-7160</identifier><identifier>EISSN: 1029-0265</identifier><identifier>DOI: 10.1080/00207160008804924</identifier><identifier>CODEN: IJCMAT</identifier><language>eng</language><publisher>Abingdon: Gordon and Breach Science Publishers</publisher><subject>A-stability ; A-stabilized Simpson's rule ; absolute stability ; collocation methods ; Exact sciences and technology ; First order initial value problem ; G.1.7 ; Mathematics ; Numerical analysis ; Numerical analysis. Scientific computation ; Ordinary differential equations ; Sciences and techniques of general use</subject><ispartof>International journal of computer mathematics, 2000-01, Vol.74 (1), p.87-96</ispartof><rights>Copyright Taylor &amp; Francis Group, LLC 2000</rights><rights>2000 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,4024,27923,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=1386512$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Sallam, S.</creatorcontrib><creatorcontrib>Naim Anwar, M.</creatorcontrib><title>Stabilized cubic c1-spline collocation method for solving first-order ordinary initial value problems</title><title>International journal of computer mathematics</title><description>This paper is concerned with a construction of a "variable" one-parameter cubic C 1 -spline collocation method for solving the initial value problem (IVP)viz where the collocation point . The presented method will be shown to be strongly unstable if β ≤ 1/2. It turns out that the proposed method is a continuous extension of the A-stabilized version of Simpson's rule introduced in [1], if β = 1. Moreover, the method is of order three, for β ∈ (1/2, 1) and is of order four, if β = 1 and y ∈ C 5 [0,b].</description><subject>A-stability</subject><subject>A-stabilized Simpson's rule</subject><subject>absolute stability</subject><subject>collocation methods</subject><subject>Exact sciences and technology</subject><subject>First order initial value problem</subject><subject>G.1.7</subject><subject>Mathematics</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Ordinary differential equations</subject><subject>Sciences and techniques of general use</subject><issn>0020-7160</issn><issn>1029-0265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2000</creationdate><recordtype>article</recordtype><recordid>eNqFkD1PwzAQhi0EEqHwA9g8sAbOjhM7Eguq-JIqMQBzZDsOGDlxZLuF8utJVJg6sNwN9zynuxehcwKXBARcAVDgpAIAIYDVlB2gjACtc6BVeYiyeZ7PwDE6ifFj5mpeZcg8J6mss9-mxXqtrMaa5HF0djBYe-e8lsn6AfcmvfsWdz7g6N3GDm-4syGm3IfWBDxVO8iwxXawyUqHN9KtDR6DV8708RQdddJFc_bbF-j17vZl-ZCvnu4flzer3JICaM5FKzpVE8M155ViJQPgTDNiGKk1KankipasNJooWYAEZUpOBa-ErjhjXbFAF7u9o4xaui7IQdvYjMH203ENKURVEjph1zvMDtNDvfz0wbVNklvnw59TEGjmZJu9ZCed_6vvWU36SsUPmfR-0g</recordid><startdate>20000101</startdate><enddate>20000101</enddate><creator>Sallam, S.</creator><creator>Naim Anwar, M.</creator><general>Gordon and Breach Science Publishers</general><general>Taylor and Francis</general><scope>IQODW</scope></search><sort><creationdate>20000101</creationdate><title>Stabilized cubic c1-spline collocation method for solving first-order ordinary initial value problems</title><author>Sallam, S. ; Naim Anwar, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i1302-78d8fb91e7c776b4540074c41e419c152a7b2545ec1ba30a0be5728768c6744f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2000</creationdate><topic>A-stability</topic><topic>A-stabilized Simpson's rule</topic><topic>absolute stability</topic><topic>collocation methods</topic><topic>Exact sciences and technology</topic><topic>First order initial value problem</topic><topic>G.1.7</topic><topic>Mathematics</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Ordinary differential equations</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sallam, S.</creatorcontrib><creatorcontrib>Naim Anwar, M.</creatorcontrib><collection>Pascal-Francis</collection><jtitle>International journal of computer mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sallam, S.</au><au>Naim Anwar, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stabilized cubic c1-spline collocation method for solving first-order ordinary initial value problems</atitle><jtitle>International journal of computer mathematics</jtitle><date>2000-01-01</date><risdate>2000</risdate><volume>74</volume><issue>1</issue><spage>87</spage><epage>96</epage><pages>87-96</pages><issn>0020-7160</issn><eissn>1029-0265</eissn><coden>IJCMAT</coden><abstract>This paper is concerned with a construction of a "variable" one-parameter cubic C 1 -spline collocation method for solving the initial value problem (IVP)viz where the collocation point . The presented method will be shown to be strongly unstable if β ≤ 1/2. It turns out that the proposed method is a continuous extension of the A-stabilized version of Simpson's rule introduced in [1], if β = 1. Moreover, the method is of order three, for β ∈ (1/2, 1) and is of order four, if β = 1 and y ∈ C 5 [0,b].</abstract><cop>Abingdon</cop><pub>Gordon and Breach Science Publishers</pub><doi>10.1080/00207160008804924</doi><tpages>10</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0020-7160
ispartof International journal of computer mathematics, 2000-01, Vol.74 (1), p.87-96
issn 0020-7160
1029-0265
language eng
recordid cdi_pascalfrancis_primary_1386512
source Taylor and Francis Science and Technology Collection
subjects A-stability
A-stabilized Simpson's rule
absolute stability
collocation methods
Exact sciences and technology
First order initial value problem
G.1.7
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
title Stabilized cubic c1-spline collocation method for solving first-order ordinary initial value problems
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-06T02%3A31%3A28IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-pascalfrancis_infor&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Stabilized%20cubic%20c1-spline%20collocation%20method%20for%20solving%20first-order%20ordinary%20initial%20value%20problems&rft.jtitle=International%20journal%20of%20computer%20mathematics&rft.au=Sallam,%20S.&rft.date=2000-01-01&rft.volume=74&rft.issue=1&rft.spage=87&rft.epage=96&rft.pages=87-96&rft.issn=0020-7160&rft.eissn=1029-0265&rft.coden=IJCMAT&rft_id=info:doi/10.1080/00207160008804924&rft_dat=%3Cpascalfrancis_infor%3E1386512%3C/pascalfrancis_infor%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-i1302-78d8fb91e7c776b4540074c41e419c152a7b2545ec1ba30a0be5728768c6744f3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true