A new approach to the construction of DIMSIMs of high order and stage order

I. Th Famelis; Zdzislaw Jackiewicz

doi:10.1016/j.apnum.2017.03.015

A new approach to the construction of DIMSIMs of high order and stage order

I. Th Famelis, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this work we describe a new approach to the construction of diagonally implicit multistage integration methods (DIMSIMs) for the numerical solution of initial value problems for ordinary differential equations (ODEs). Differential Evolution, a very popular computational intelligence technique is employed to construct type 1 and type 2 methods with better or equivalent characteristics to the methods presented in the literature. The numerical results in selected problems justify this argument.

Original language	English (US)
Pages (from-to)	79-93
Number of pages	15
Journal	Applied Numerical Mathematics
Volume	119
DOIs	https://doi.org/10.1016/j.apnum.2017.03.015
State	Published - Sep 1 2017

Keywords

Differential evolution
Error control
Error estimation
General linear methods
Nordsieck representation

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/j.apnum.2017.03.015

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abstract = "In this work we describe a new approach to the construction of diagonally implicit multistage integration methods (DIMSIMs) for the numerical solution of initial value problems for ordinary differential equations (ODEs). Differential Evolution, a very popular computational intelligence technique is employed to construct type 1 and type 2 methods with better or equivalent characteristics to the methods presented in the literature. The numerical results in selected problems justify this argument.",

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AU - Jackiewicz, Zdzislaw

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N2 - In this work we describe a new approach to the construction of diagonally implicit multistage integration methods (DIMSIMs) for the numerical solution of initial value problems for ordinary differential equations (ODEs). Differential Evolution, a very popular computational intelligence technique is employed to construct type 1 and type 2 methods with better or equivalent characteristics to the methods presented in the literature. The numerical results in selected problems justify this argument.

AB - In this work we describe a new approach to the construction of diagonally implicit multistage integration methods (DIMSIMs) for the numerical solution of initial value problems for ordinary differential equations (ODEs). Differential Evolution, a very popular computational intelligence technique is employed to construct type 1 and type 2 methods with better or equivalent characteristics to the methods presented in the literature. The numerical results in selected problems justify this argument.

KW - Differential evolution

KW - Error control

KW - Error estimation

KW - General linear methods

KW - Nordsieck representation

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

A new approach to the construction of DIMSIMs of high order and stage order

Abstract

Keywords

ASJC Scopus subject areas

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