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A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations

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Abstract

In this research, we study the numerical solution of fractional Lane-Emden type equations, which emerge mainly in astrophysics applications. We propose a numerical approach making use of Legendre wavelets and the quasilinearization technique. The nonlinear term in fractional Lane-Emden type equations is iteratively linearized using the quasilinearization technique. The linearized equations are then solved using the Legendre wavelet collocation method. The proposed method is quite effective to overcome the singularity in fractional Lane-Emden type equations. Convergence and error analysis of the proposed method are given. We solve some test problems to compare the effectiveness of the proposed method with some other numerical methods in the literature.

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Authors and Affiliations

  1. Department of Mathematics, Izmir Institute of Technology, Izmir, Türkiye

    Fatih İdiz, Gamze Tanoğlu & Nasser Aghazadeh

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  1. Fatih İdiz
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  2. Gamze Tanoğlu
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  3. Nasser Aghazadeh
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All authors contributed to the preparation of the text and presentation of the results; they also read and approved the final manuscript.

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Correspondence to Nasser Aghazadeh.

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İdiz, F., Tanoğlu, G. & Aghazadeh, N. A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations. Numer Algor 95, 181–206 (2024). https://doi.org/10.1007/s11075-023-01568-z

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