Numerical methods in inverse problems
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Abstract
Abstract
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 \(L_2\) 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.
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@article{Abbasov2026Analytical,
title = {Analytical and Numerical Solution of the Heat Conduction Equation in a Cylindrical Domain: Convergence Analysis and Bessel Collocation Method},
author = {Zafar Duman Abbasov and Y. H. Youssri and Waleed Mohammed Abdelfattah and Ibrahim Alraddadi and Hijaz Ahmad},
journal = {International Journal of Analysis and Applications},
year = {2026},
doi = {10.28924/2291-8639-24-2026-237},
url = {https://doi.org/10.28924/2291-8639-24-2026-237}
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