Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method
In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in th...
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Published in | Mathematical methods in the applied sciences Vol. 44; no. 3; pp. 2671 - 2681 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
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01.02.2021
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Abstract | In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in the literature, and the obtained results are compared with Sinc‐collocation method. These results show the reliability and effectiveness of the proposed method. The proposed method does not require discretization like other numerical methods. Moreover, the convergence region can easily be controlled. The use of OHAM is simple and straightforward. |
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AbstractList | In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in the literature, and the obtained results are compared with Sinc‐collocation method. These results show the reliability and effectiveness of the proposed method. The proposed method does not require discretization like other numerical methods. Moreover, the convergence region can easily be controlled. The use of OHAM is simple and straightforward. |
Author | Nawaz, Rashid Jleli, Mohamed Akbar, Muhammad Agarwal, Praveen |
Author_xml | – sequence: 1 givenname: Praveen orcidid: 0000-0001-7556-8942 surname: Agarwal fullname: Agarwal, Praveen email: goyal.praveen2011@gmail.com organization: Institute of Mathematics and Mathematical Modeling – sequence: 2 givenname: Muhammad surname: Akbar fullname: Akbar, Muhammad organization: Abdul Wali Khan University Mardan – sequence: 3 givenname: Rashid orcidid: 0000-0002-4773-8446 surname: Nawaz fullname: Nawaz, Rashid organization: Abdul Wali Khan University Mardan – sequence: 4 givenname: Mohamed orcidid: 0000-0002-6095-5875 surname: Jleli fullname: Jleli, Mohamed organization: King Saud University |
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Cites_doi | 10.1016/j.icheatmasstransfer.2008.02.010 10.1016/j.aej.2014.04.004 10.1155/2013/278097 10.3233/IFS-120732 10.12988/ijcms.2013.13052 10.22436/jmcs.05.04.02 10.1155/2014/725648 10.4236/am.2011.29152 10.11648/j.ijtam.20190506.14 10.5899/2013/cna-00186 |
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References | 2004; 155 2016; 6 2018; 5 2011; 2 2013; 2 2019; 5 2013; 2013 2007; 192 2008; 9 2014; 26 2017 2008; 35 2014; 2014 2013 2013; 8 2011; 5 2012; 5 2014; 53 Ghazanfari B (e_1_2_8_18_1) 2013; 2013 Berenguer MI (e_1_2_8_8_1) 2017 e_1_2_8_13_1 e_1_2_8_15_1 Matinfar M (e_1_2_8_3_1) 2014; 26 Maleknejad K (e_1_2_8_10_1) 2004; 155 Hashmia MS (e_1_2_8_17_1) 2016; 6 Hesameddini E (e_1_2_8_20_1) 2013; 2 Yusufoğlu E (e_1_2_8_2_1) 2007; 192 Akbar M (e_1_2_8_19_1) 2019; 5 Hesameddini ESMAIL (e_1_2_8_9_1) 2013; 2 Al‐Smadi M (e_1_2_8_6_1) 2013; 8 Rabbani M (e_1_2_8_12_1) 2012; 5 Davari A (e_1_2_8_11_1) 2011; 5 e_1_2_8_4_1 Almousa M (e_1_2_8_16_1) 2013 Herişanu N (e_1_2_8_14_1) 2008; 9 Loh JR (e_1_2_8_5_1) 2018; 5 Biazar J (e_1_2_8_7_1) 2011; 2 |
References_xml | – volume: 26 start-page: 1095 issue: 3 year: 2014 end-page: 1102 article-title: Homotopy analysis method for systems of integro‐differential equations publication-title: Journal of Intelligent & Fuzzy Systems – volume: 53 start-page: 751 issue: 3 year: 2014 end-page: 755 article-title: Optimal homotopy asymptotic method for solving Volterra integral equation of first kind publication-title: Alex Eng J – volume: 6 start-page: 162 issue: 4S year: 2016 end-page: 166 article-title: Exact solution of Fredholmintegro‐differential equations using optimal homotopy asymptotic method publication-title: Journal of Applied Environmental and Biological Sciences – volume: 5 start-page: 2356 issue: 12 year: 2011 end-page: 2361 article-title: Solution of system of Fredholm integro differential equations by Adomian decomposition method publication-title: Australian Journal of Basic and Applied Sciences – volume: 2 start-page: 1105 issue: 9 year: 2011 end-page: 1113 article-title: A strong method for solving systems of integro‐differential equations publication-title: Applied Mathematics – volume: 2 start-page: 1 issue: 7 year: 2013 end-page: 9 article-title: Solving systems of linear Volterra integro‐differential equations by using Sinc‐collocation method publication-title: International Journal of Mathematical Engineering and Science – start-page: 1 year: 2017 end-page: 18 article-title: Solution of systems of integro‐differential equations using numerical treatment of fixed point publication-title: Journal of Computational and Applied Mathematics – start-page: 1 year: 2013 end-page: 6 article-title: Optimal homotopy asymptotic method for solving the linear Fredholm integral equations of the first kind publication-title: Abstract and Applied Analysis – volume: 2013 start-page: 1 year: 2013 end-page: 15 article-title: Optimal homotopy asymptotic method for solving system of Fredholm integral equations publication-title: Communications in Numerical Analysis – volume: 155 start-page: 317 issue: 2 year: 2004 end-page: 328 article-title: Solving linear integro‐differential equations system by using rationalized Haar functions method publication-title: Appl Math Comput – volume: 5 start-page: 1117 year: 2018 end-page: 1124 article-title: A new numerical scheme for solving system of Volterra integro‐differential equation publication-title: Alexandria Engineering Journal – volume: 5 start-page: 258 issue: 4 year: 2012 end-page: 264 article-title: Solution of Fredholm integro‐differential equations system by modified decomposition method publication-title: Journal of Mathematics and Computer Science – volume: 5 start-page: 100 issue: 6 year: 2019 end-page: 112 article-title: Optimum solutions of Fredholm and Volterra integro‐differential equations publication-title: International Journal of Theoretical and Applied Mathematics – volume: 8 start-page: 531 issue: 11 year: 2013 end-page: 540 article-title: Solution of system of Fredholm integro‐differential equations by RKHS method publication-title: International Journal of Contemporary Mathematical Sciences – volume: 2014 start-page: 1 year: 2014 end-page: 5 article-title: Solving systems of Volterra integral and integrodifferential equations with proportional delays by differential transformation method publication-title: Journal of Mathematics – volume: 9 start-page: 229 issue: 3 year: 2008 end-page: 236 article-title: A new analytical approach to nonlinear vibration of an electrical machine publication-title: Proceedings of the Romanian Academy‐Series A – volume: 35 start-page: 710 issue: 6 year: 2008 end-page: 715 article-title: Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer publication-title: International Communications in Heat and Mass Transfer – volume: 192 start-page: 51 issue: 1 year: 2007 end-page: 55 article-title: An efficient algorithm for solving integro‐differential equations system publication-title: Appl Math Comput – ident: e_1_2_8_13_1 doi: 10.1016/j.icheatmasstransfer.2008.02.010 – start-page: 1 year: 2017 ident: e_1_2_8_8_1 article-title: Solution of systems of integro‐differential equations using numerical treatment of fixed point publication-title: Journal of Computational and Applied Mathematics contributor: fullname: Berenguer MI – ident: e_1_2_8_15_1 doi: 10.1016/j.aej.2014.04.004 – start-page: 1 year: 2013 ident: e_1_2_8_16_1 article-title: Optimal homotopy asymptotic method for solving the linear Fredholm integral equations of the first kind publication-title: Abstract and Applied Analysis doi: 10.1155/2013/278097 contributor: fullname: Almousa M – volume: 9 start-page: 229 issue: 3 year: 2008 ident: e_1_2_8_14_1 article-title: A new analytical approach to nonlinear vibration of an electrical machine publication-title: Proceedings of the Romanian Academy‐Series A contributor: fullname: Herişanu N – volume: 155 start-page: 317 issue: 2 year: 2004 ident: e_1_2_8_10_1 article-title: Solving linear integro‐differential equations system by using rationalized Haar functions method publication-title: Appl Math Comput contributor: fullname: Maleknejad K – volume: 26 start-page: 1095 issue: 3 year: 2014 ident: e_1_2_8_3_1 article-title: Homotopy analysis method for systems of integro‐differential equations publication-title: Journal of Intelligent & Fuzzy Systems doi: 10.3233/IFS-120732 contributor: fullname: Matinfar M – volume: 8 start-page: 531 issue: 11 year: 2013 ident: e_1_2_8_6_1 article-title: Solution of system of Fredholm integro‐differential equations by RKHS method publication-title: International Journal of Contemporary Mathematical Sciences doi: 10.12988/ijcms.2013.13052 contributor: fullname: Al‐Smadi M – volume: 5 start-page: 258 issue: 4 year: 2012 ident: e_1_2_8_12_1 article-title: Solution of Fredholm integro‐differential equations system by modified decomposition method publication-title: Journal of Mathematics and Computer Science doi: 10.22436/jmcs.05.04.02 contributor: fullname: Rabbani M – ident: e_1_2_8_4_1 doi: 10.1155/2014/725648 – volume: 2 start-page: 1105 issue: 9 year: 2011 ident: e_1_2_8_7_1 article-title: A strong method for solving systems of integro‐differential equations publication-title: Applied Mathematics doi: 10.4236/am.2011.29152 contributor: fullname: Biazar J – volume: 6 start-page: 162 issue: 4 year: 2016 ident: e_1_2_8_17_1 article-title: Exact solution of Fredholmintegro‐differential equations using optimal homotopy asymptotic method publication-title: Journal of Applied Environmental and Biological Sciences contributor: fullname: Hashmia MS – volume: 5 start-page: 1117 year: 2018 ident: e_1_2_8_5_1 article-title: A new numerical scheme for solving system of Volterra integro‐differential equation publication-title: Alexandria Engineering Journal contributor: fullname: Loh JR – volume: 5 start-page: 100 issue: 6 year: 2019 ident: e_1_2_8_19_1 article-title: Optimum solutions of Fredholm and Volterra integro‐differential equations publication-title: International Journal of Theoretical and Applied Mathematics doi: 10.11648/j.ijtam.20190506.14 contributor: fullname: Akbar M – volume: 192 start-page: 51 issue: 1 year: 2007 ident: e_1_2_8_2_1 article-title: An efficient algorithm for solving integro‐differential equations system publication-title: Appl Math Comput contributor: fullname: Yusufoğlu E – volume: 2 start-page: 1 issue: 7 year: 2013 ident: e_1_2_8_9_1 article-title: Solving systems of linear Volterra integro‐differential equations by using Sinc‐collocation method publication-title: International Journal of Mathematical Engineering and Science contributor: fullname: Hesameddini ESMAIL – volume: 2 start-page: 1 issue: 7 year: 2013 ident: e_1_2_8_20_1 article-title: Solving systems of linear Volterra integro‐differential equations by using Sinc‐collocation method publication-title: International Journal of Mathematical Engineering and Science contributor: fullname: Hesameddini E – volume: 5 start-page: 2356 issue: 12 year: 2011 ident: e_1_2_8_11_1 article-title: Solution of system of Fredholm integro differential equations by Adomian decomposition method publication-title: Australian Journal of Basic and Applied Sciences contributor: fullname: Davari A – volume: 2013 start-page: 1 year: 2013 ident: e_1_2_8_18_1 article-title: Optimal homotopy asymptotic method for solving system of Fredholm integral equations publication-title: Communications in Numerical Analysis doi: 10.5899/2013/cna-00186 contributor: fullname: Ghazanfari B |
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SubjectTerms | approximate solutions Asymptotic methods Collocation methods Differential equations Numerical methods optimal homotopy asymptotic method system of Volterra integro‐differential equations Volterra integral equations |
Title | Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method |
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