Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equations

In this article, a new method is generated to solve nonlinear Lane–Emden type equations using Legendre, Hermite and Laguerre wavelets. We are interested to note that these wavelets will give same solutions with good accuracy. Theorems on convergence analysis are stated and proved on the spaces, whic...

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Bibliographic Details
Published in:Applied mathematics and computation 2017-12, Vol.315, p.591-602
Main Authors: Shiralashetti, S.C., Kumbinarasaiah, S.
Format: Article
Language:English
Subjects:
Collocation method
Hermite wavelet
Isomorphism
Laguerre wavelet
Lane–Emden type equations
Legendre wavelet
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Summary:In this article, a new method is generated to solve nonlinear Lane–Emden type equations using Legendre, Hermite and Laguerre wavelets. We are interested to note that these wavelets will give same solutions with good accuracy. Theorems on convergence analysis are stated and proved on the spaces, which are created by Legendre, Hermite and Laguerre wavelets bases and justified these spaces are equivalent to polynomial linear space generated by general polynomial basis. The main idea for obtaining numerical solutions depends on converting the differential equation with initial and boundary conditions into a system of linear or nonlinear algebraic equations with unknown coefficients. A very high level of accuracy reflects the reliability of this scheme for such problems.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2017.07.071