Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations
In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm–Volterra integrodifferential equations. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions in which the const...
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| Veröffentlicht in: | Neural computing & applications 2017-07, Vol.28 (7), p.1591-1610 |
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| creator | Abu Arqub, Omar |
| description | In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm–Volterra integrodifferential equations. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions in which the constraint initial condition is satisfied, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their
r
-cut representation form in the Hilbert space
W
2
2
Ω
⊕
W
2
2
Ω
. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. Finally, the utilized results show that the present method and simulated annealing provide a good scheduling methodology to solve such fuzzy equations. |
| doi_str_mv | 10.1007/s00521-015-2110-x |
| format | Article |
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r
-cut representation form in the Hilbert space
W
2
2
Ω
⊕
W
2
2
Ω
. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. Finally, the utilized results show that the present method and simulated annealing provide a good scheduling methodology to solve such fuzzy equations.</description><identifier>ISSN: 0941-0643</identifier><identifier>EISSN: 1433-3058</identifier><identifier>DOI: 10.1007/s00521-015-2110-x</identifier><language>eng</language><publisher>London: Springer London</publisher><subject>Adaptation ; Artificial Intelligence ; Computational Biology/Bioinformatics ; Computational Science and Engineering ; Computer Science ; Computer simulation ; Data Mining and Knowledge Discovery ; Hilbert space ; Image Processing and Computer Vision ; Kernel functions ; Original Article ; Probability and Statistics in Computer Science ; Scheduling ; Simulated annealing ; Volterra integral equations</subject><ispartof>Neural computing & applications, 2017-07, Vol.28 (7), p.1591-1610</ispartof><rights>The Natural Computing Applications Forum 2015</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-c2cf6a8895f826439cff61bd9622898340734dd5c9a905c930923cd109c03ae13</citedby><cites>FETCH-LOGICAL-c316t-c2cf6a8895f826439cff61bd9622898340734dd5c9a905c930923cd109c03ae13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00521-015-2110-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00521-015-2110-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Abu Arqub, Omar</creatorcontrib><title>Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations</title><title>Neural computing & applications</title><addtitle>Neural Comput & Applic</addtitle><description>In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm–Volterra integrodifferential equations. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions in which the constraint initial condition is satisfied, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their
r
-cut representation form in the Hilbert space
W
2
2
Ω
⊕
W
2
2
Ω
. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. Finally, the utilized results show that the present method and simulated annealing provide a good scheduling methodology to solve such fuzzy equations.</description><subject>Adaptation</subject><subject>Artificial Intelligence</subject><subject>Computational Biology/Bioinformatics</subject><subject>Computational Science and Engineering</subject><subject>Computer Science</subject><subject>Computer simulation</subject><subject>Data Mining and Knowledge Discovery</subject><subject>Hilbert space</subject><subject>Image Processing and Computer Vision</subject><subject>Kernel functions</subject><subject>Original Article</subject><subject>Probability and Statistics in Computer Science</subject><subject>Scheduling</subject><subject>Simulated annealing</subject><subject>Volterra integral equations</subject><issn>0941-0643</issn><issn>1433-3058</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1UL1OwzAQthBIlMIDsFliDtzZSRqPVUUBqRILsFrGsdOUNG7tBLWdeAfekCfBpQwsLHfD93f3EXKJcI0Ao5sAkDFMALOEIUKyOSIDTDlPOGTFMRmASCOap_yUnIWwAIA0L7IBacelWnWqq11LnaXerLwre123FX0zvjUNVU3lfN3Nl9Q6T4Nr3veg7Xe7LZ16U85ds_z6-HxxTWe8V7RuO1NFk9pa403b1aqhZt3_RIRzcmJVE8zF7x6S5-nt0-Q-mT3ePUzGs0RzzLtEM21zVRQiswWLRwttbY6vpcgZK0TBUxjxtCwzLZSAODkIxnWJIDRwZZAPydXBN76z7k3o5ML1vo2REgVmAhnyUWThgaW9C8EbK1e-Xiq_lQhyX6s81CpjrXJfq9xEDTtoQuS2lfF_nP8VfQMzqH4S</recordid><startdate>20170701</startdate><enddate>20170701</enddate><creator>Abu Arqub, Omar</creator><general>Springer London</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170701</creationdate><title>Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations</title><author>Abu Arqub, Omar</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-c2cf6a8895f826439cff61bd9622898340734dd5c9a905c930923cd109c03ae13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Adaptation</topic><topic>Artificial Intelligence</topic><topic>Computational Biology/Bioinformatics</topic><topic>Computational Science and Engineering</topic><topic>Computer Science</topic><topic>Computer simulation</topic><topic>Data Mining and Knowledge Discovery</topic><topic>Hilbert space</topic><topic>Image Processing and Computer Vision</topic><topic>Kernel functions</topic><topic>Original Article</topic><topic>Probability and Statistics in Computer Science</topic><topic>Scheduling</topic><topic>Simulated annealing</topic><topic>Volterra integral equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Abu Arqub, Omar</creatorcontrib><collection>CrossRef</collection><jtitle>Neural computing & applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Abu Arqub, Omar</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations</atitle><jtitle>Neural computing & applications</jtitle><stitle>Neural Comput & Applic</stitle><date>2017-07-01</date><risdate>2017</risdate><volume>28</volume><issue>7</issue><spage>1591</spage><epage>1610</epage><pages>1591-1610</pages><issn>0941-0643</issn><eissn>1433-3058</eissn><abstract>In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm–Volterra integrodifferential equations. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions in which the constraint initial condition is satisfied, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their
r
-cut representation form in the Hilbert space
W
2
2
Ω
⊕
W
2
2
Ω
. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. Finally, the utilized results show that the present method and simulated annealing provide a good scheduling methodology to solve such fuzzy equations.</abstract><cop>London</cop><pub>Springer London</pub><doi>10.1007/s00521-015-2110-x</doi><tpages>20</tpages></addata></record> |
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| language | eng |
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| subjects | Adaptation Artificial Intelligence Computational Biology/Bioinformatics Computational Science and Engineering Computer Science Computer simulation Data Mining and Knowledge Discovery Hilbert space Image Processing and Computer Vision Kernel functions Original Article Probability and Statistics in Computer Science Scheduling Simulated annealing Volterra integral equations |
| title | Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations |
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