Analytical technique for neutral delay differential equations with proportional and constant delays
Neutral delay differential equations (NDDEs) are a type of delay differential equations (DDEs) that arise in numerous areas of applied sciences and play a vital role in mathematical modelling of real-life phenomena. Some techniques have experienced difficulties in finding the approximate analytical...
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my.utm.916002021-07-11T14:30:24Z http://eprints.utm.my/id/eprint/91600/ Analytical technique for neutral delay differential equations with proportional and constant delays Maan, Normah Barde, Aminu QA Mathematics Neutral delay differential equations (NDDEs) are a type of delay differential equations (DDEs) that arise in numerous areas of applied sciences and play a vital role in mathematical modelling of real-life phenomena. Some techniques have experienced difficulties in finding the approximate analytical solution which converges rapidly to the exact solution of these equations. In this paper, an analytical approach is proposed for solving linear and nonlinear NDDEs with proportional and constant delays based on the homotopy analysis method (HAM) and natural transform method where the nonlinear terms are simply calculated as a series of, He’s polynomial. The proposed method produces solutions in the form of a rapidly convergent series which leads to the exact solution from only a few numbers of iterations. Some illustrative examples are solved, and the convergence analysis of the proposed techniques was also provided. The obtained results reveal that the approach is very effective and efficient in handling both linear and nonlinear NDDEs with proportional and constant delays and can also be used in various types of linear and nonlinear problems. International Scientific Research Publications 2020-03 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/91600/1/NormahMaan2020_AnalyticalTechniqueforNeutralDelayDifferential.pdf Maan, Normah and Barde, Aminu (2020) Analytical technique for neutral delay differential equations with proportional and constant delays. Journal of Mathematics and Computer Science, 20 (4). pp. 334-348. ISSN 2008-949X http://dx.doi.org/10.22436/jmcs.020.04.07 DOI:10.22436/jmcs.020.04.07 |
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QA Mathematics Maan, Normah Barde, Aminu Analytical technique for neutral delay differential equations with proportional and constant delays |
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Neutral delay differential equations (NDDEs) are a type of delay differential equations (DDEs) that arise in numerous areas of applied sciences and play a vital role in mathematical modelling of real-life phenomena. Some techniques have experienced difficulties in finding the approximate analytical solution which converges rapidly to the exact solution of these equations. In this paper, an analytical approach is proposed for solving linear and nonlinear NDDEs with proportional and constant delays based on the homotopy analysis method (HAM) and natural transform method where the nonlinear terms are simply calculated as a series of, He’s polynomial. The proposed method produces solutions in the form of a rapidly convergent series which leads to the exact solution from only a few numbers of iterations. Some illustrative examples are solved, and the convergence analysis of the proposed techniques was also provided. The obtained results reveal that the approach is very effective and efficient in handling both linear and nonlinear NDDEs with proportional and constant delays and can also be used in various types of linear and nonlinear problems. |
format |
Article |
author |
Maan, Normah Barde, Aminu |
author_facet |
Maan, Normah Barde, Aminu |
author_sort |
Maan, Normah |
title |
Analytical technique for neutral delay differential equations with proportional and constant delays |
title_short |
Analytical technique for neutral delay differential equations with proportional and constant delays |
title_full |
Analytical technique for neutral delay differential equations with proportional and constant delays |
title_fullStr |
Analytical technique for neutral delay differential equations with proportional and constant delays |
title_full_unstemmed |
Analytical technique for neutral delay differential equations with proportional and constant delays |
title_sort |
analytical technique for neutral delay differential equations with proportional and constant delays |
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International Scientific Research Publications |
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2020 |
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http://eprints.utm.my/id/eprint/91600/1/NormahMaan2020_AnalyticalTechniqueforNeutralDelayDifferential.pdf http://eprints.utm.my/id/eprint/91600/ http://dx.doi.org/10.22436/jmcs.020.04.07 |
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