Numerical Differentiation by Integrated Series Expansion (NDBISE) in the Context of Ordinary Differential Equation Estimation Problems

Numerical Differentiation by Integrated Series Expansion (NDBISE) in the Context of Ordinary Differential Equation Estimation Problems | 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 Numerical Differentiation by Integrated Series Expansion (NDBISE) in the Context of Ordinary Differential Equation Estimation Problems Oliver Strebel This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5465961/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 Parameter or model estimation of ordinary differential equations (ODE) nowadays frequently involves the numerical calculation of derivatives from noisy data. This study presents a novel differentiation method (NDBISE) for such calculations. The method was benchmarked against 57 differential equations and compared to five numerical differentiation methods: central finite differences, numerical derivatives using the Friedrichs mollifier, weak differentiation using this mollifier, first order polynomial approximation and spectral derivatives. For the latter method, a novel criterion is presented that allows the determination of the low pass filter parameter. The hyperparameters of all these methods are optimized in order to get a reasonable comparison. The resilience against larger noise or fewer data points per time interval is examined. It turns out that the novel method is overall superior to the other methods. The derivative for the 42 real world data points of the Hudson bay lynx hare data (years 1900-1920) is also calculated. The results match the derivative of a curve fit to the data points astonishingly close. Using a Savitsky-Golay filter, the method can be leveraged, to calculate second and third order derivatives, so that the results are close to the theoretically expected outcome. The paper references a GitHub project that contains code and an application manual to reproduce all figures of the result section from ODE state data. Computational Mathematics model estimation numerical differentiation ordinary differential equation parameter estimation system identification time series analysis 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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