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Efficient spectral ultraspherical-dual-Petrov–Galerkin algorithms for the direct solution of (2n+1)th-order linear differential equations

Author

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  • Doha, E.H.
  • Abd-Elhameed, W.M.

Abstract

Some efficient and accurate algorithms based on ultraspherical-dual-Petrov–Galerkin method are developed and implemented for solving (2n+1)th-order linear elliptic differential equations in one variable subject to homogeneous and nonhomogeneous boundary conditions using a spectral discretization. The key idea to the efficiency of our algorithms is to use trial functions satisfying the underlying boundary conditions of the differential equations and the test functions satisfying the dual boundary conditions. The method leads to linear systems with specially structured matrices that can be efficiently inverted. Numerical results are presented to demonstrate the efficiency of our proposed algorithms.

Suggested Citation

  • Doha, E.H. & Abd-Elhameed, W.M., 2009. "Efficient spectral ultraspherical-dual-Petrov–Galerkin algorithms for the direct solution of (2n+1)th-order linear differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3221-3242.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:11:p:3221-3242
    DOI: 10.1016/j.matcom.2009.03.011
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    Cited by:

    1. Guimarães, O. & Labecca, W. & Piqueira, José Roberto C., 2020. "Generalized operational matrices and error bounds for polynomial basis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 258-272.
    2. Abdelkawy, M.A. & Alyami, S.A., 2021. "Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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