Application of the spectral galarkin method for solving integral heat transfer equations based on chebeshev and hermit polynomial bases

Application of the spectral galarkin method for solving integral heat transfer equations based on chebeshev and hermit polynomial bases | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 13 June 2025 V1 Latest version Share on Application of the spectral galarkin method for solving integral heat transfer equations based on chebeshev and hermit polynomial bases Authors : EZATULLAH HALEEM 0009-0007-6153-1111 [email protected] , AHADKHAN PIAWARI , and IRSHAD SALARZAI Authors Info & Affiliations https://doi.org/10.22541/au.174979636.69175222/v1 221 views 108 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This study proposes a robust and high-fidelity numerical framework for solving the integral form of the one-dimensional (1D) unsteady heat conduction (HC) equation. The framework is built upon the spectral Galerkin method utilizing Chebyshev and Hermite polynomials as orthogonal basis functions for spatial discretization By reformulating the classical parabolic heat equation into an equivalent integral representation using Green’s function and the Laplace transform the problem gains enhanced smoothness and numerical stability-particularly in the presence of sharp gradients or boundary layers (Atkinson 1997; Polyanin & Manzhirov 2008) The spectral Galerkin method renowned for its exponential convergence when applied to smooth problems (Boyd 2001; Shen et al. 2011) was implemented using both polynomial bases Comparative numerical experiments indicate that Chebyshev polynomials exhibit superior accuracy and faster convergence compared to Hermite polynomials within bounded domains In contrast, Hermite polynomials despite their theoretical strength on unbounded intervals displayed slower convergence and higher approximation errors when constrained to finite domains. Error analyses conducted for multiple polynomial degrees confirmed the spectral nature of the convergence with Chebyshev-based solutions consistently outperforming their Hermite counterparts. As a result the study concludes that Chebyshev polynomials are the more appropriate choice for solving bounded-domain heat conduction problems using the integral Galerkin spectral method The proposed methodology not only ensures stability and high-order accuracy for classical thermal problems but also offers a promising foundation for future extensions to nonlinear time-dependent and multidimensional heat transfer systems Supplementary Material File (springer_ready_spectral_galerkin_heat_transfer.docx) Download 530.68 KB Information & Authors Information Version history V1 Version 1 13 June 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords boundary value problems chebyshev polynomials heat conduction hermite polynomials integral equations numerical analysis orthogonal basis functions spectral galerkin method spectral methods thermal diffusion Authors Affiliations EZATULLAH HALEEM 0009-0007-6153-1111 [email protected] Kabul University of Medical Sciences Abu Ali Ibn Sina View all articles by this author AHADKHAN PIAWARI Kabul University of Medical Sciences Abu Ali Ibn Sina View all articles by this author IRSHAD SALARZAI Kabul University of Medical Sciences Abu Ali Ibn Sina View all articles by this author Metrics & Citations Metrics Article Usage 221 views 108 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation EZATULLAH HALEEM, AHADKHAN PIAWARI, IRSHAD SALARZAI. Application of the spectral galarkin method for solving integral heat transfer equations based on chebeshev and hermit polynomial bases. Authorea . 13 June 2025. DOI: https://doi.org/10.22541/au.174979636.69175222/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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