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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)231-255
Number of pages25
JournalInvolve
Volume13
Issue number2
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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