General Linear Method with F-property and Inherent Quadratic Stability for Solving Stiff differential systems

General Linear Method with F-property and Inherent Quadratic Stability for Solving Stiff differential systems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article General Linear Method with F-property and Inherent Quadratic Stability for Solving Stiff differential systems Sakshi Gautam, Ram K. Pandey This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8711138/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract This work introduces a new class of general linear methods (GLMs) for solving systems of time-dependent differential equations, based on the Nordsieck input vector and equipped with the \emph{F}-property. The proposed methods are characterized by $r=s=p+1$ and satisfy inherent quadratic stability criteria. GLMs with the \emph{F}-property offer a natural extension of Runge–Kutta schemes with the \emph{first same as last} (FSAL) property and provide improved efficiency over non-FSAL methods with the same number of stages. We develop implicit GLMs with the \emph{F}-property that are well suited for stiff differential systems arising from semi-discretization of partial differential equations (PDEs). The theoretical framework needed for constructing these schemes is presented, along with a key modification in the matrix equivalence necessary for enforcing IQS in the presence of the \emph{F}-property. The proposed classes are then tested on three different test problems. The results of the numerical simulations carried out for all the three problems reveal a good agreement with the reference solutions. The results are interpreted using computation of error norms, estimated orders, and work precision diagrams. General linear methods F-Property Inherent Quadratic Stability Time-dependent differential equation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 21 Feb, 2026 Reviews received at journal 02 Feb, 2026 Reviewers agreed at journal 02 Feb, 2026 Reviewers invited by journal 02 Feb, 2026 Editor assigned by journal 02 Feb, 2026 Submission checks completed at journal 02 Feb, 2026 First submitted to journal 27 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8711138","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":584580706,"identity":"6f9227d5-992c-46b9-9a9e-2d78c2b7c5f9","order_by":0,"name":"Sakshi Gautam","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBUlEQVRIie3PMUvDQBTA8VcOLkvAVcmQr/CgcCIe6eDH6HLl4GUSMjoUjBTasatfQujUOXBwXYpZAy7poquQxcHBS7sJiXETvP90HO/HuwPw+f5kHBigZMA4B5VJdzN6KAYQCk4EqSX5AALmzB04AJrjXS+JV1Y3WWaiy4BTXWOZPK2M2zKX0y6Ce7LRI6bjqwXfocIXvd3PHLF0m3cRSJcsxGuNJliet0QUjoxy00ni9duiCZHdb07kWYvy0E+goiIK8Yah4daRIhHVD1uweiVHqCXkiFaicltUz1/iNY2b8FMyLK24+LhLJqJMD/X7XHY/7Huz46QaOt42+c2wz+fz/Y++AFz/XYDubr5FAAAAAElFTkSuQmCC","orcid":"","institution":"Dr. Hari Singh Gour University","correspondingAuthor":true,"prefix":"","firstName":"Sakshi","middleName":"","lastName":"Gautam","suffix":""},{"id":584580707,"identity":"63fc126c-7e9f-4588-a89f-3bc96e6c98b2","order_by":1,"name":"Ram K. 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