Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity
The main focus of this paper was to find the approximate solution of a class of second-order multi-pantograph delay differential equations with singularity. We used the shifted version of Vieta–Lucas polynomials with some symmetries as the main base to develop a collocation approach for solving the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/12/2370 |
| _version_ | 1797500306297192448 |
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| author | Mohammad Izadi Şuayip Yüzbaşı Khursheed J. Ansari |
| author_facet | Mohammad Izadi Şuayip Yüzbaşı Khursheed J. Ansari |
| author_sort | Mohammad Izadi |
| collection | DOAJ |
| description | The main focus of this paper was to find the approximate solution of a class of second-order multi-pantograph delay differential equations with singularity. We used the shifted version of Vieta–Lucas polynomials with some symmetries as the main base to develop a collocation approach for solving the aforementioned differential equations. Moreover, an error bound of the present approach by using the maximum norm was computed and an error estimation technique based on the residual function is presented. Finally, the validity and applicability of the presented collocation scheme are shown via four numerical test examples. |
| first_indexed | 2024-03-10T03:00:00Z |
| format | Article |
| id | doaj.art-71403747a6de4e2888fa239b9b053b43 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T03:00:00Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-71403747a6de4e2888fa239b9b053b432023-11-23T10:46:13ZengMDPI AGSymmetry2073-89942021-12-011312237010.3390/sym13122370Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with SingularityMohammad Izadi0Şuayip Yüzbaşı1Khursheed J. Ansari2Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman 76169-14111, IranDepartment of Mathematics, Faculty of Science, Akdeniz University, Antalya TR 07058, TurkeyDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaThe main focus of this paper was to find the approximate solution of a class of second-order multi-pantograph delay differential equations with singularity. We used the shifted version of Vieta–Lucas polynomials with some symmetries as the main base to develop a collocation approach for solving the aforementioned differential equations. Moreover, an error bound of the present approach by using the maximum norm was computed and an error estimation technique based on the residual function is presented. Finally, the validity and applicability of the presented collocation scheme are shown via four numerical test examples.https://www.mdpi.com/2073-8994/13/12/2370collocation methoderror analysismulti-pantograph delay differential equationssingularityVieta–Lucas functions |
| spellingShingle | Mohammad Izadi Şuayip Yüzbaşı Khursheed J. Ansari Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity Symmetry collocation method error analysis multi-pantograph delay differential equations singularity Vieta–Lucas functions |
| title | Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity |
| title_full | Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity |
| title_fullStr | Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity |
| title_full_unstemmed | Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity |
| title_short | Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity |
| title_sort | application of vieta lucas series to solve a class of multi pantograph delay differential equations with singularity |
| topic | collocation method error analysis multi-pantograph delay differential equations singularity Vieta–Lucas functions |
| url | https://www.mdpi.com/2073-8994/13/12/2370 |
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