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

Krainer, Thomas; Zhou, Chenzhang

doi:10.2140/involve.2020.13.231

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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

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.

Keywords

numerical methods for ODEs, initial value problems

Mathematical Subject Classification 2010

Primary: 65L05

Supplementary material

Matlab code for the quadratic Taylor method

Milestones

Received: 19 March 2019

Accepted: 25 February 2020

Published: 30 March 2020

Communicated by Kenneth S. Berenhaut

Authors

Thomas Krainer
Penn State Altoona Altoona, PA United States

Chenzhang Zhou
Penn State Altoona Altoona, PA United States

Vol. 13, No. 2, 2020