Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden Type
The aim of this study is presentan effective and correct technique for solving differential equations ofLane-Emden type as initial value problems. In this work, a numerical method namedas the Fibonacci polynomial approximation method, for the approximate solutionof differential equations of Lane-Emd...
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Sakarya University
2019-06-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/649406 |
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| author | Musa Çakmak |
| author_facet | Musa Çakmak |
| author_sort | Musa Çakmak |
| collection | DOAJ |
| description | The aim of this study is presentan effective and correct technique for solving differential equations ofLane-Emden type as initial value problems. In this work, a numerical method namedas the Fibonacci polynomial approximation method, for the approximate solutionof differential equations of Lane-Emden type in term of Fibonacci polynomialsare studied. A matrix equation can be solved depending on the matrix relationsof Fibonacci polynomials and their derivatives, and their reduced form to thesolution of differential equations of Lane-Emden type, characterized by asystem of algebraic equations with the unknown Fibonacci coefficients. Also, numericalresults with comparisons are given to confirm the reliability of the proposed methodfor differential equations of Lane-Emden type. |
| format | Article |
| id | doaj-art-c852fc8d2a10455181e8cc6325534a82 |
| institution | OA Journals |
| issn | 2147-835X |
| language | English |
| publishDate | 2019-06-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-c852fc8d2a10455181e8cc6325534a822025-08-20T01:57:44ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2019-06-0123347848510.16984/saufenbilder.34499128Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden TypeMusa Çakmak0MUSTAFA KEMAL ÜNİVERSİTESİThe aim of this study is presentan effective and correct technique for solving differential equations ofLane-Emden type as initial value problems. In this work, a numerical method namedas the Fibonacci polynomial approximation method, for the approximate solutionof differential equations of Lane-Emden type in term of Fibonacci polynomialsare studied. A matrix equation can be solved depending on the matrix relationsof Fibonacci polynomials and their derivatives, and their reduced form to thesolution of differential equations of Lane-Emden type, characterized by asystem of algebraic equations with the unknown Fibonacci coefficients. Also, numericalresults with comparisons are given to confirm the reliability of the proposed methodfor differential equations of Lane-Emden type.https://dergipark.org.tr/tr/download/article-file/649406diferansiyel fark denklemlerifibonacci polinomlarılane-emden denklemioperasyonel matrispolinom yaklaşımıdifferential- difference equationsfibonacci polynomialslane-emden equationoperational matrixpolynomial approach |
| spellingShingle | Musa Çakmak Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden Type Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi diferansiyel fark denklemleri fibonacci polinomları lane-emden denklemi operasyonel matris polinom yaklaşımı differential- difference equations fibonacci polynomials lane-emden equation operational matrix polynomial approach |
| title | Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden Type |
| title_full | Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden Type |
| title_fullStr | Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden Type |
| title_full_unstemmed | Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden Type |
| title_short | Fibonacci Operational Matrix Algorithm For Solving Differential Equations Of Lane-Emden Type |
| title_sort | fibonacci operational matrix algorithm for solving differential equations of lane emden type |
| topic | diferansiyel fark denklemleri fibonacci polinomları lane-emden denklemi operasyonel matris polinom yaklaşımı differential- difference equations fibonacci polynomials lane-emden equation operational matrix polynomial approach |
| url | https://dergipark.org.tr/tr/download/article-file/649406 |
| work_keys_str_mv | AT musacakmak fibonaccioperationalmatrixalgorithmforsolvingdifferentialequationsoflaneemdentype |