An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral
A new exponential Chebyshev operational matrix of derivatives based on Chebyshev polynomials of second kind (ESC) is investigated. The new operational matrix of derivatives of the ESC functions is derived and introduced for solving high-order linear ordinary differential equations with variable coef...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X16300505 |
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| author | Mohamed A. Ramadan Kamal R. Raslan Talaat S. El Danaf Mohamed A. Abd El Salam |
| author_facet | Mohamed A. Ramadan Kamal R. Raslan Talaat S. El Danaf Mohamed A. Abd El Salam |
| author_sort | Mohamed A. Ramadan |
| collection | DOAJ |
| description | A new exponential Chebyshev operational matrix of derivatives based on Chebyshev polynomials of second kind (ESC) is investigated. The new operational matrix of derivatives of the ESC functions is derived and introduced for solving high-order linear ordinary differential equations with variable coefficients in unbounded domain using the collocation method. As an application the introduced method is used to evaluate Dawson's integral by solving its differential equation. The corresponding differential equation to Dawson's integral is a boundary value problem with conditions tends to infinity. The obtained numerical results are compared with the exact solution and showed good accuracy. |
| first_indexed | 2024-12-13T15:08:33Z |
| format | Article |
| id | doaj.art-dcb821ab02ad487a90ed1940f7243927 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-13T15:08:33Z |
| publishDate | 2017-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-dcb821ab02ad487a90ed1940f72439272022-12-21T23:40:56ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2017-04-0125219720510.1016/j.joems.2016.07.001An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integralMohamed A. Ramadan0Kamal R. Raslan1Talaat S. El Danaf2Mohamed A. Abd El Salam3Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, EgyptMathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptDepartment of Mathematics and Statistics, Taibah University Madinah Munawwarah, Saudi ArabiaMathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptA new exponential Chebyshev operational matrix of derivatives based on Chebyshev polynomials of second kind (ESC) is investigated. The new operational matrix of derivatives of the ESC functions is derived and introduced for solving high-order linear ordinary differential equations with variable coefficients in unbounded domain using the collocation method. As an application the introduced method is used to evaluate Dawson's integral by solving its differential equation. The corresponding differential equation to Dawson's integral is a boundary value problem with conditions tends to infinity. The obtained numerical results are compared with the exact solution and showed good accuracy.http://www.sciencedirect.com/science/article/pii/S1110256X16300505Exponential second kind Chebyshev functionsHigh-order ordinary differential equationsCollocation methodDawson's integral |
| spellingShingle | Mohamed A. Ramadan Kamal R. Raslan Talaat S. El Danaf Mohamed A. Abd El Salam An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral Journal of the Egyptian Mathematical Society Exponential second kind Chebyshev functions High-order ordinary differential equations Collocation method Dawson's integral |
| title | An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral |
| title_full | An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral |
| title_fullStr | An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral |
| title_full_unstemmed | An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral |
| title_short | An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral |
| title_sort | exponential chebyshev second kind approximation for solving high order ordinary differential equations in unbounded domains with application to dawson s integral |
| topic | Exponential second kind Chebyshev functions High-order ordinary differential equations Collocation method Dawson's integral |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X16300505 |
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