Power time numerical integration algorithm for nonlinear fractional differential equations

被引：5

作者：

Nasuno, Hiroshi ^{[1
]}

Shimizu, Nobuyuki ^{[2
]}

机构：

[1] Iwaki Meisei Univ, Sci & Engn Div, Fukushima 9708551, Japan

[2] Iwaki Meisei Univ, Dept Mech Syst & Engn, Fukushima 9708551, Japan

来源：

JOURNAL OF VIBRATION AND CONTROL | 2008年 / 14卷 / 9-10期

关键词：

fractional differential equation; numerical integration; power time; newmark-beta method; nonlinear viscoelasticity; fractional derivative of displacement squared;

D O I：

10.1177/1077546307087449

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

A numerical integration algorithm to solve single-degree-of-freedom nonlinear fractional differential equations (NFDEs) is proposed, by introducing the power time concept and by means of the Newmark-beta method one step scheme. An NFDE involving fractional derivatives of the displacement and the displacement squared is solved numerically, using the proposed power time algorithm. The error analysis of the algorithm, and the contribution of the displacement squared fractional derivative term to the solution of NFDE, are also given.

引用

页码：1313 / 1332

页数：20

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