Legendre wavelet collocation method with quasilinearization technique for fractional differential equations
tarafından
İdiz, Fatih, author.
Başlık
:
Legendre wavelet collocation method with quasilinearization technique for fractional differential equations
Yazar
:
İdiz, Fatih, author.
Yazar Ek Girişi
:
İdiz, Fatih, author.
Fiziksel Tanımlama
:
viii, 61 leaves: charts;+ 1 computer laser optical disc.
Özet
:
We aim to present numerical methods based on Legendre wavelets and quasilinearization technique for fractional Lane-Emden type equations and time-fractional Fisher’s equation. The Lane-Emden equation is a second order singular non-linear ordinary differential equation, which is useful for modelling many astrophysical phenomena such as the distribution of stars in star clusters and star formation in molecular clouds. The Fisher’s equation is a non-linear reaction-diffusion equation that models the spread of mutant genes in a population. We start with a brief discussion of the purpose of studying fractional differential equations. Then some practical aspects of wavelets are explained. We also give introductory definitions and properties of fractional calculus and Legendre wavelets. Using Legendre wavelets and quasilinearization technique, we derive numerical methods for fractional Lane-Emden type equations and time-fractional Fisher’s equation. Moreover, the convergence analysis of both methods is studied. Some problems are solved to evaluate the efficiency of the proposed methods. Test problems show that the proposed methods are very effective.
Konu Başlığı
:
Fractional differential equations.
Quasilinearization
Yazar Ek Girişi
:
Tanoğlu, Gamze,
Tüzel Kişi Ek Girişi
:
İzmir Institute of Technology. Mathematics.
Tek Biçim Eser Adı
:
Thesis (Master)--İzmir Institute of Technology: Mathematics.
İzmir Institute of Technology: Mathematics--Thesis (Master).
Elektronik Erişim
:
Library | Materyal Türü | Demirbaş Numarası | Yer Numarası | Durumu/İade Tarihi |
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IYTE Library | Tez | T002656 | QA372 .I19 2022 | Tez Koleksiyonu |