Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind
In this work, we employed the Laplace transform of right-sided distributions in conjunction with the power series method to obtain distributional solutions to the modified Bessel equation and its related equation, whose coefficients contain the parameters <inline-formula><math xmlns="h...
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/7/1725 |
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| author | Waritsara Thongthai Kamsing Nonlaopon Somsak Orankitjaroen Chenkuan Li |
| author_facet | Waritsara Thongthai Kamsing Nonlaopon Somsak Orankitjaroen Chenkuan Li |
| author_sort | Waritsara Thongthai |
| collection | DOAJ |
| description | In this work, we employed the Laplace transform of right-sided distributions in conjunction with the power series method to obtain distributional solutions to the modified Bessel equation and its related equation, whose coefficients contain the parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>. We demonstrated that the solutions can be expressed as finite linear combinations of the Dirac delta function and its derivatives, with the specific form depending on the values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>. |
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| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T05:30:31Z |
| publishDate | 2023-04-01 |
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| spelling | doaj.art-3ee88256d67d4168a06d0dc3ba52bbc52023-11-17T17:09:46ZengMDPI AGMathematics2227-73902023-04-01117172510.3390/math11071725Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second KindWaritsara Thongthai0Kamsing Nonlaopon1Somsak Orankitjaroen2Chenkuan Li3Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, ThailandDepartment of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, CanadaIn this work, we employed the Laplace transform of right-sided distributions in conjunction with the power series method to obtain distributional solutions to the modified Bessel equation and its related equation, whose coefficients contain the parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>. We demonstrated that the solutions can be expressed as finite linear combinations of the Dirac delta function and its derivatives, with the specific form depending on the values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/11/7/1725Dirac delta functiondistributional solutiongeneralized solutionsLaplace transformpower series solution |
| spellingShingle | Waritsara Thongthai Kamsing Nonlaopon Somsak Orankitjaroen Chenkuan Li Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind Mathematics Dirac delta function distributional solution generalized solutions Laplace transform power series solution |
| title | Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind |
| title_full | Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind |
| title_fullStr | Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind |
| title_full_unstemmed | Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind |
| title_short | Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind |
| title_sort | generalized solutions of ordinary differential equations related to the chebyshev polynomial of the second kind |
| topic | Dirac delta function distributional solution generalized solutions Laplace transform power series solution |
| url | https://www.mdpi.com/2227-7390/11/7/1725 |
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