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Chebyshev delta shaped and Chebyshev pseudo-spectral methods for solutions of differential equations

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  • Akyildiz, Fahir Talay
  • Vajravelu, Kuppalapalle
  • Tunç, Cemil
  • Abraham, John

Abstract

In this paper we introduce a new Chebyshev delta-shaped function (CDSF) and establish its relationship with Chebyshev polynomials in interpolation problems. We first prove that CDSF is indeed form a basis for a Haar space. We then derive the conditions for the selection of suitable collocation points. Next, we introduce and develop Chebyshev delta-shaped pseudo-spectral method. Error bounds on discrete L2−norm and Sobolev norm Hp are presented for the Chebyshev pseudo-spectral method. Tests to find approximate solutions for the Poisson, Poisson-Boltzmann equations and Stokes second problem and comparisons of the predictions using the following methods are presented:

Suggested Citation

  • Akyildiz, Fahir Talay & Vajravelu, Kuppalapalle & Tunç, Cemil & Abraham, John, 2025. "Chebyshev delta shaped and Chebyshev pseudo-spectral methods for solutions of differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 236(C), pages 52-69.
    • Handle: RePEc:eee:matcom:v:236:y:2025:i:c:p:52-69
    DOI: 10.1016/j.matcom.2025.03.034
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