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

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  • Shiralashetti, S.C.
  • Kumbinarasaiah, S.

Abstract

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.

Suggested Citation

  • Shiralashetti, S.C. & Kumbinarasaiah, S., 2017. "Theoretical study on continuous polynomial wavelet bases through wavelet series collocation method for nonlinear Lane–Emden type equations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 591-602.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:591-602
    DOI: 10.1016/j.amc.2017.07.071
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    Cited by:

    1. Sunil Kumar & Ali Ahmadian & Ranbir Kumar & Devendra Kumar & Jagdev Singh & Dumitru Baleanu & Mehdi Salimi, 2020. "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets," Mathematics, MDPI, vol. 8(4), pages 1-22, April.
    2. Izadi, Mohammad, 2021. "A discontinuous finite element approximation to singular Lane-Emden type equations," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    3. Korkut, Sıla Övgü, 2023. "An accurate and efficient numerical solution for the generalized Burgers–Huxley equation via Taylor wavelets method: Qualitative analyses and Applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 324-341.
    4. S., Kumbinarasaiah & G., Manohara & G., Hariharan, 2023. "Bernoulli wavelets functional matrix technique for a system of nonlinear singular Lane Emden equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 133-165.

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