Analytical and Numerical Solution of the Heat Conduction Equation in a Cylindrical Domain: Convergence Analysis and Bessel Collocation Method
International Journal of Analysis and Applications, cilt.24, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 24
- Basım Tarihi: 2026
- Doi Numarası: 10.28924/2291-8639-24-2026-237
- Dergi Adı: International Journal of Analysis and Applications
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Anahtar Kelimeler: Bessel collocation method, Bessel functions, convergence analysis, cylindrical domain, Fourier-Bessel series, heat conduction equation, time-dependent boundary conditions
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Karadeniz Teknik Üniversitesi Adresli: Hayır
Özet
This paper presents both analytical and numerical approaches for solving the non-homogeneous heat conduction equation in a cylindrical domain with time-dependent polynomial and harmonic boundary conditions. The analytical solution is constructed using the superposition principle and Fourier-Bessel series expansion, with rigorous proofs of convergence in the L2 norm and asymptotic stability. For numerical implementation, we develop a Bessel Collocation Method that achieves spectral accuracy with moderate computational cost. Theoretical error estimates are derived, showing exponential convergence in space and second-order accuracy in time. Numerical experiments confirm the theoretical predictions, with absolute errors decreasing from 10−2 to 10−15 as the number of basis functions increases. The results demonstrate that the proposed framework provides reliable solutions for heat transfer problems with complex boundary regimes in circular geometries.