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Abstract
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We present an explicit one-step numerical method of third order that is error-free on
autonomous scalar Riccati equations such as the logistic equation. The method
replaces the differential equation by its quadratic Taylor polynomial in each step and
utilizes the exact solution of that equation for the calculation of the next
approximation.
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Keywords
numerical methods for ODEs, initial value problems
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Mathematical Subject Classification 2010
Primary: 65L05
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Milestones
Received: 19 March 2019
Accepted: 25 February 2020
Published: 30 March 2020
Communicated by Kenneth S. Berenhaut
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