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Legendre wavelet Galerkin method for solving ordinary differential equations with non-analytic solution

Author

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  • F. Mohammadi
  • M.M. Hosseini
  • Syed Tauseef Mohyud-Din

Abstract

In this article, the Legendre wavelet operational matrix of integration is used to solve boundary ordinary differential equations with non-analytic solution. Although the standard Galerkin method using Legendre polynomials does not work well for solving ordinary differential equations in which at least one of the coefficient functions or solution function is not analytic, it is shown that the Legendre wavelet Galerkin method is very efficient and suitable for solving this kind of problems. Several numerical examples are given to illustrate the efficiency and performance of the presented method.

Suggested Citation

  • F. Mohammadi & M.M. Hosseini & Syed Tauseef Mohyud-Din, 2011. "Legendre wavelet Galerkin method for solving ordinary differential equations with non-analytic solution," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(4), pages 579-585.
    • Handle: RePEc:taf:tsysxx:v:42:y:2011:i:4:p:579-585
    DOI: 10.1080/00207721003658194
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    Cited by:

    1. Usman, M. & Hamid, M. & Zubair, T. & Haq, R.U. & Wang, W. & Liu, M.B., 2020. "Novel operational matrices-based method for solving fractional-order delay differential equations via shifted Gegenbauer polynomials," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    2. Zubair, Tamour & Lu, Tiao & Usman, Muhammad, 2021. "Higher dimensional semi-relativistic time-fractional Vlasov-Maxwell code for numerical simulation based on linear polarization and 2D Landau damping instability," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    3. Singh, Jitendra & Jitendra, & Rai, Kabindra Nath, 2020. "Legendre wavelet based numerical solution of variable latent heat moving boundary problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 485-500.
    4. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    5. Aydin Secer & Selvi Altun, 2018. "A New Operational Matrix of Fractional Derivatives to Solve Systems of Fractional Differential Equations via Legendre Wavelets," Mathematics, MDPI, vol. 6(11), pages 1-16, November.

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