Polynomial Collocation Methods Based on Successive Integration Technique for Solving Neutral Delay Differential Equations
This paper presents a new approach of using polynomials such as Hermite, Bernoulli, Chebyshev, Fibonacci and Bessel to solve neutral delay differential equations. The proposed method is based on the truncated polynomial expansion of the function together with collocation points and successive integr...
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| Format: | Article |
| Language: | English |
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Accademia Piceno Aprutina dei Velati
2023-12-01
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| Series: | Ratio Mathematica |
| Subjects: | |
| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/1417 |
| _version_ | 1797371562836361216 |
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| author | Kayelvizhi C. Emimal Kanaga Pushpam A. |
| author_facet | Kayelvizhi C. Emimal Kanaga Pushpam A. |
| author_sort | Kayelvizhi C. |
| collection | DOAJ |
| description | This paper presents a new approach of using polynomials such as Hermite, Bernoulli, Chebyshev, Fibonacci and Bessel to solve neutral delay differential equations. The proposed method is based on the truncated polynomial expansion of the function together with collocation points and successive integration techniques. This method reduces the given equation to a system of non-linear equations with unknown polynomial coefficients which can be easily calculated. The convergence of the proposed method is discussed with several mild conditions. Numerical examples are considered to demonstrate the efficiency of the method. The numerical results reveal that the proposed new approach gives better results than the conventional operational matrix approach of the polynomial collocation method. It demonstrates the reliability and efficiency of this method for solving linear and nonlinear neutral delay differential equations. |
| first_indexed | 2024-03-08T18:21:04Z |
| format | Article |
| id | doaj.art-711294c5e2154890a361a2e0b84ac275 |
| institution | Directory Open Access Journal |
| issn | 1592-7415 2282-8214 |
| language | English |
| last_indexed | 2024-03-08T18:21:04Z |
| publishDate | 2023-12-01 |
| publisher | Accademia Piceno Aprutina dei Velati |
| record_format | Article |
| series | Ratio Mathematica |
| spelling | doaj.art-711294c5e2154890a361a2e0b84ac2752023-12-30T21:04:20ZengAccademia Piceno Aprutina dei VelatiRatio Mathematica1592-74152282-82142023-12-0148010.23755/rm.v48i0.1417887Polynomial Collocation Methods Based on Successive Integration Technique for Solving Neutral Delay Differential EquationsKayelvizhi C.0Emimal Kanaga Pushpam A.1Research Scholar Department of Mathematics Bishop Heber College Affiliated to "Bharathidasan University" Tiruchirappalli Tamilnadu, IndiaAssociate Professor Department of Mathematics Bishop Heber College Affiliated to "Bharathidasan University" Tiruchirappalli Tamilnadu, IndiaThis paper presents a new approach of using polynomials such as Hermite, Bernoulli, Chebyshev, Fibonacci and Bessel to solve neutral delay differential equations. The proposed method is based on the truncated polynomial expansion of the function together with collocation points and successive integration techniques. This method reduces the given equation to a system of non-linear equations with unknown polynomial coefficients which can be easily calculated. The convergence of the proposed method is discussed with several mild conditions. Numerical examples are considered to demonstrate the efficiency of the method. The numerical results reveal that the proposed new approach gives better results than the conventional operational matrix approach of the polynomial collocation method. It demonstrates the reliability and efficiency of this method for solving linear and nonlinear neutral delay differential equations.http://eiris.it/ojs/index.php/ratiomathematica/article/view/1417polynomialscollocation methodsuccessive integration techniqueneutral delay differential equations. |
| spellingShingle | Kayelvizhi C. Emimal Kanaga Pushpam A. Polynomial Collocation Methods Based on Successive Integration Technique for Solving Neutral Delay Differential Equations Ratio Mathematica polynomials collocation method successive integration technique neutral delay differential equations. |
| title | Polynomial Collocation Methods Based on Successive Integration Technique for Solving Neutral Delay Differential Equations |
| title_full | Polynomial Collocation Methods Based on Successive Integration Technique for Solving Neutral Delay Differential Equations |
| title_fullStr | Polynomial Collocation Methods Based on Successive Integration Technique for Solving Neutral Delay Differential Equations |
| title_full_unstemmed | Polynomial Collocation Methods Based on Successive Integration Technique for Solving Neutral Delay Differential Equations |
| title_short | Polynomial Collocation Methods Based on Successive Integration Technique for Solving Neutral Delay Differential Equations |
| title_sort | polynomial collocation methods based on successive integration technique for solving neutral delay differential equations |
| topic | polynomials collocation method successive integration technique neutral delay differential equations. |
| url | http://eiris.it/ojs/index.php/ratiomathematica/article/view/1417 |
| work_keys_str_mv | AT kayelvizhic polynomialcollocationmethodsbasedonsuccessiveintegrationtechniqueforsolvingneutraldelaydifferentialequations AT emimalkanagapushpama polynomialcollocationmethodsbasedonsuccessiveintegrationtechniqueforsolvingneutraldelaydifferentialequations |