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

Akyildiz F. T., Vajravelu K., Tunç C., Abraham J.

Mathematics and Computers in Simulation, cilt.236, ss.52-69, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 236
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/j.matcom.2025.03.034
  • Dergi Adı: Mathematics and Computers in Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH
  • Sayfa Sayıları: ss.52-69
  • Anahtar Kelimeler: Chebyshev delta-shaped functions, Chebyshev pseudo-spectral method (collocation method), Chebyshev-delta shaped pseudo-spectral method, Non-singular matrix, Non-smooth boundary condition, Poisson -Boltzmann equations (free energy of highly charged molecules)
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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: 1. Chebyshev pseudo-spectral method, 2. Cosine-sine delta-shaped pseudo-spectral method, and 3. Cosine-sine pseudo-spectral method. Excellent convergent and stable results are obtained by using our newly defined Chebyshev delta-shaped basis functions and this is documented for the first time.