A Constructive Algebraic Framework for Exterior Integration Equations: Theory, Computation, and Applications

A Constructive Algebraic Framework for Exterior Integration Equations: Theory, Computation, and Applications | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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. 20 October 2025 V1 Latest version Share on A Constructive Algebraic Framework for Exterior Integration Equations: Theory, Computation, and Applications Authors : Dongqi Liu 0009-0006-4018-9292 and shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations 155 views 126 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This paper establishes a comprehensive constructive algebraic framework for solving exterior integration equations, building upon the theory of exterior integration as the dual operation to exterior differentiation. In contrast to the well-developed the ory for exterior differential equations, a systematic treatment for their integral counterparts remains underdeveloped. We define the exterior integration algebraic closure Kint through a recursive adjunction process that incorporates explicit solu tions to exterior integration equations, including particular so lutions via fiber integration, homogeneous solution bases, har monic forms, and fundamental solutions. Weprovide a unified explicit solution representation for lin ear exterior integration equations and develop efficient com putational algorithms with rigorous numerical validation. The framework applies to exterior integration equations in fiber bundle structures and maintains consistency with Stokes’ the orem, de Rham cohomology, and Hodge theory.Detailed mathematical formulations, constructive proofs,computational methodologies, and numerical examples are presented to demonstrate the consistency and utility of the theory. The main contributions include: (1) a constructive theoretical framework for exterior integration equations, (2) explicit solution representations with complete convergence analysis, (3) efficient computational algorithms with certified error bounds, (4) rigorous numerical validation protocols, and (5) detailed applications to physically significant problems. Supplementary Material File (exterior_integral_equation1.pdf) Download 238.70 KB Information & Authors Information Version history V1 Version 1 20 October 2025 DOI 10.22541/au.176099573.39573779/v1 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords characteristic classes constructive solutions de rham cohomology exterior integration algebraic closure exterior integration equations fiber integration hodge theory numerical validation stokes' theorem Authors Affiliations Dongqi Liu 0009-0006-4018-9292 View all articles by this author shifa liu 0009-0003-6570-2812 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 155 views 126 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Dongqi Liu, shifa liu. A Constructive Algebraic Framework for Exterior Integration Equations: Theory, Computation, and Applications. Authorea . 20 October 2025. 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