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

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

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 236, issue C, 52-69

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:

Keywords: Chebyshev pseudo-spectral method (collocation method); Chebyshev delta-shaped functions; Chebyshev-delta shaped pseudo-spectral method; Non-singular matrix; Poisson -Boltzmann equations (free energy of highly charged molecules); Non-smooth boundary condition (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:236:y:2025:i:c:p:52-69

DOI: 10.1016/j.matcom.2025.03.034

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