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Application of wavelet collocation method for hyperbolic partial differential equations via matrices

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  • Singh, Somveer
  • Patel, Vijay Kumar
  • Singh, Vineet Kumar

Abstract

In this work, we developed an efficient computational method based on Legendre and Chebyshev wavelets to find an approximate solution of one dimensional hyperbolic partial differential equations (HPDEs) with the given initial conditions. The operational matrices of integration for Legendre and Chebyshev wavelets are derived and utilized to transform the given PDE into the linear system of equations by combining collocation method. Convergence analysis and error estimation associated to the presented idea are also investigated under several mild conditions. Numerical experiments confirm that the proposed method has good accuracy and efficiency. Moreover, the use of Legendre and Chebyshev wavelets are found to be accurate, simple and fast.

Suggested Citation

  • Singh, Somveer & Patel, Vijay Kumar & Singh, Vineet Kumar, 2018. "Application of wavelet collocation method for hyperbolic partial differential equations via matrices," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 407-424.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:407-424
    DOI: 10.1016/j.amc.2017.09.043
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    References listed on IDEAS

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    1. Razzaghi, M. & Yousefi, S., 2000. "Legendre wavelets direct method for variational problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(3), pages 185-192.
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    Cited by:

    1. Haifa Bin Jebreen & Fairouz Tchier, 2020. "On the Numerical Simulation of HPDEs Using θ -Weighted Scheme and the Galerkin Method," Mathematics, MDPI, vol. 9(1), pages 1-13, December.
    2. Kumar, Yashveer & Yadav, Poonam & Singh, Vineet Kumar, 2023. "Distributed order Gauss-Quadrature scheme for distributed order fractional sub-diffusion model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Singh, Somveer & Devi, Vinita & Tohidi, Emran & Singh, Vineet Kumar, 2020. "An efficient matrix approach for two-dimensional diffusion and telegraph equations with Dirichlet boundary conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Kumar, Yashveer & Singh, Vineet Kumar, 2021. "Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 531-569.
    5. Neslihan Ozdemir & Aydin Secer & Mustafa Bayram, 2019. "The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative," Mathematics, MDPI, vol. 7(6), pages 1-15, May.
    6. Sun, Lin & Chen, Yiming, 2021. "Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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