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2020 An explicit third-order one-step method for autonomous scalar initial value problems of first order based on quadratic Taylor approximation
Thomas Krainer, Chenzhang Zhou
Involve 13(2): 231-255 (2020). DOI: 10.2140/involve.2020.13.231

Abstract

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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Thomas Krainer. Chenzhang Zhou. "An explicit third-order one-step method for autonomous scalar initial value problems of first order based on quadratic Taylor approximation." Involve 13 (2) 231 - 255, 2020. https://doi.org/10.2140/involve.2020.13.231

Information

Received: 19 March 2019; Accepted: 25 February 2020; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07184483
MathSciNet: MR4080493
Digital Object Identifier: 10.2140/involve.2020.13.231

Subjects:
Primary: 65L05

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 2 • 2020
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