Advances in Overcoming Methodological Limitations of HAM and HPM: OM-HPM

Advances in Overcoming Methodological Limitations of HAM and HPM: OM-HPM | 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 Advances in Overcoming Methodological Limitations of HAM and HPM: OM-HPM Tapas Roy, Dilip Kumar Maiti This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8222560/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Despite the success of the Homotopy Analysis Method (HAM) and related semi-analytical techniques, there were several methodological challenges remains long-standing opened, particularly the absence of rigorous mathematical theorems to choose optimal auxiliary linear operator, basis functions, and initial guesses as well as the lack of globally convergent series for IVPs. This work summarizes our contributions to addressed these challenges with comprehensive theoretical and numerical demonstrations. Also extend this work by comparing HAM, HPM, and their variants with our technique, showing how different choices of linear operators yield distinct kinds of series solutions and influence convergence, which is a crucial aspect often overlooked. Established scientific merit of HAM/HPM through our contribution, which was questionable. Applied Mathematics Homotopy Analysis Method Homotopy Perturbation Method Semi-Analytical Method Computational Method Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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. 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