Constructive Exterior Differential Algebraic Framework for Nonlinear Exterior Differential Equations

Constructive Exterior Differential Algebraic Framework for Nonlinear Exterior Differential Equations | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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 Constructive Exterior Differential Algebraic Framework for Nonlinear Exterior Differential Equations Authors : Dongqi Liu 0009-0006-4018-9292 and shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations 151 views 150 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract 本文建立了一个建设性的微分代数框架，用于获得大类非线性外微分方程（EDE）的显式解析解。我们定义了非线性外部微分代数闭包 K NLEDE，这是一种通过递归附加过程构建的微分闭域扩展，该过程结合了线性化 EDE、多索引根扩展、统一根和一组建设性定义的非线性特殊微分形式的解。在这个闭包中，我们证明了具有解析系数的 n 阶非线性 EDE 的解，满足外部柯西-科瓦列夫斯卡娅定理的条件，允许统一表示。该框架严格解决了 EDE 固有的多维和无限维挑战，同时保留了外部微积分的分级代数结构。我们提供建设性证明，通过适当的正则化推导非线性校正系数的显式组合表达式，并在适当的函数空间中建立微分形式的收敛标准。提出了具有复杂性分析的详细算法，包括稳定性保证和具有认证误差边界的自适应精度控制。建立了严格的验证框架，在离散外部微积分中采用区间算术和交叉验证与高阶数值方法进行交叉验证。这项工作表明，虽然初等函数中的闭式解 1 对于许多非线性 EDE 来说是不可能的，但显式解析解存在于适当扩展和建设性定义的非线性外部微分代数闭包 K NLEDE 中。该框架被证明与经典 EDE 理论一致，同时扩展了解空间以包括非线性特殊微分形式和尊重外部代数属性的组合校正结构。 Supplementary Material File (nonlinear_exterior_differential.pdf) Download 505.96 KB Information & Authors Information Version history V1 Version 1 20 October 2025 DOI 10.22541/au.176098899.94784544/v1 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords adaptive precision certified computation combinatorial analysis differential algebraic closure explicit solution exterior calculus homotopy methods nonlinear exterior differential equations numerical computation special differential forms 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 151 views 150 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Dongqi Liu, shifa liu. Constructive Exterior Differential Algebraic Framework for Nonlinear Exterior Differential Equations. Authorea . 20 October 2025. DOI: https://doi.org/10.22541/au.176098899.94784544/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 . 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