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- W4379980429 abstract "Abstract In this paper, extended Legendre wavelet is considered. The solution of Bessel's differential equation has been obtained by extended Legendre wavelet technique and the convergence analysis of its solution has been studied. Two new extended Legendre wavelet estimators $E_{mu^k,0}(f)$, $E_{mu^k,M}(f)$ and two new moduli of continuity $ Wbig(big(f-(S_{mu^{k},0}f)big),frac{1}{mu^{k}}big) , Wbig( big(f-(S_{mu^{k},M}f)big),frac{1}{mu^{k}}big) $ of solution function with first derivative $ f^{'} $ belong to $H_{2}^{alpha} [0,1)$ of order $0<alpha leq 1$, has been developed. These estimators and moduli of continuity are new and best possible in wavelet analysis. Extended Legendre wavelet collocation method has been developed to solve Bessel differential equations with unknown extended Legendre wavelet coefficients. In this process, Bessel differential equations are reduced into a system of algebraic equations and these equations are solved by collocation method. To show the utility and validity of the suggested approach, three Bessel type differential equations are solved. The solution obtained by proposed method are compared to their exact solutions. The absolute errors are negligible. This demonstrates the applicability and accuracy of the methodology presented in this paper. Mathematics Subject Classification:42C40, 65T60, 45G10, 45B05." @default.
- W4379980429 created "2023-06-10" @default.
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- W4379980429 date "2023-06-09" @default.
- W4379980429 modified "2023-09-27" @default.
- W4379980429 title "Approximation and moduli of continuity of a function with first derivative f' belonging to Ha2[0,1) and solution of Bessel differential equation by ExtendedLegendre wavelet technique" @default.
- W4379980429 doi "https://doi.org/10.21203/rs.3.rs-3034916/v1" @default.
- W4379980429 hasPublicationYear "2023" @default.
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