English

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

Numerical Analysis 2020-04-01 v1 Classical Analysis and ODEs

Abstract

We present an explicit 1-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

Cite

@article{arxiv.1805.04782,
  title  = {An explicit third-order one-step method for autonomous scalar initial value problems of first order based on adaptive quadratic Taylor approximation},
  author = {Thomas Krainer and Chenzhang Zhou},
  journal= {arXiv preprint arXiv:1805.04782},
  year   = {2020}
}
R2 v1 2026-06-23T01:53:01.895Z