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

doi:10.2140/involve.2020.13.231

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

Division of Mathematics & Natural Sciences (Altoona)

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	231-255
Number of pages	25
Journal	Involve
Volume	13
Issue number	2
DOIs	https://doi.org/10.2140/involve.2020.13.231
State	Published - 2020

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.2140/involve.2020.13.231

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title = "An explicit third-order one-step method for autonomous scalar initial value problems of first order based on quadratic taylor approximation",

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

Abstract

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