Vol. 13, No. 2, 2020

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An explicit third-order one-step method for autonomous scalar initial value problems of first order based on quadratic Taylor approximation

Thomas Krainer and Chenzhang Zhou

Vol. 13 (2020), No. 2, 231–255

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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numerical methods for ODEs, initial value problems
Mathematical Subject Classification 2010
Primary: 65L05
Supplementary material

Matlab code for the quadratic Taylor method

Received: 19 March 2019
Accepted: 25 February 2020
Published: 30 March 2020

Communicated by Kenneth S. Berenhaut
Thomas Krainer
Penn State Altoona
Altoona, PA
United States
Chenzhang Zhou
Penn State Altoona
Altoona, PA
United States