A kind of product integration scheme for solving fractional ordinary differential equations

Jingjun Zhao; Yu Li; Yang Xu

doi:10.1016/j.apnum.2018.10.014

A kind of product integration scheme for solving fractional ordinary differential equations

Jingjun Zhao
, Yu Li
, Yang Xu^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology
Heilongjiang Bayi Agricultural University

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

10 Scopus citations

Abstract

In this paper, we construct a kind of product integration scheme for the nonlinear fractional ordinary differential equation. We design the scheme by considering the equivalent Volterra integral equation and using the idea of local Fourier expansion. We prove the high accuracy property of the new scheme and provide the stability analysis. Numerical experiments demonstrate the effectiveness of the scheme.

Original language	English
Pages (from-to)	279-292
Number of pages	14
Journal	Applied Numerical Mathematics
Volume	136
DOIs	https://doi.org/10.1016/j.apnum.2018.10.014
State	Published - Feb 2019

Keywords

Caputo fractional derivative
Fractional differential equation
Local Fourier expansion
Product integration

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10.1016/j.apnum.2018.10.014

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title = "A kind of product integration scheme for solving fractional ordinary differential equations",

abstract = "In this paper, we construct a kind of product integration scheme for the nonlinear fractional ordinary differential equation. We design the scheme by considering the equivalent Volterra integral equation and using the idea of local Fourier expansion. We prove the high accuracy property of the new scheme and provide the stability analysis. Numerical experiments demonstrate the effectiveness of the scheme.",

keywords = "Caputo fractional derivative, Fractional differential equation, Local Fourier expansion, Product integration",

author = "Jingjun Zhao and Yu Li and Yang Xu",

note = "Publisher Copyright: {\textcopyright} 2018 IMACS",

year = "2019",

month = feb,

doi = "10.1016/j.apnum.2018.10.014",

language = "英语",

volume = "136",

pages = "279--292",

journal = "Applied Numerical Mathematics",

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T1 - A kind of product integration scheme for solving fractional ordinary differential equations

AU - Zhao, Jingjun

AU - Li, Yu

AU - Xu, Yang

PY - 2019/2

Y1 - 2019/2

N2 - In this paper, we construct a kind of product integration scheme for the nonlinear fractional ordinary differential equation. We design the scheme by considering the equivalent Volterra integral equation and using the idea of local Fourier expansion. We prove the high accuracy property of the new scheme and provide the stability analysis. Numerical experiments demonstrate the effectiveness of the scheme.

AB - In this paper, we construct a kind of product integration scheme for the nonlinear fractional ordinary differential equation. We design the scheme by considering the equivalent Volterra integral equation and using the idea of local Fourier expansion. We prove the high accuracy property of the new scheme and provide the stability analysis. Numerical experiments demonstrate the effectiveness of the scheme.

KW - Caputo fractional derivative

KW - Fractional differential equation

KW - Local Fourier expansion

KW - Product integration

UR - https://www.scopus.com/pages/publications/85056273170

U2 - 10.1016/j.apnum.2018.10.014

DO - 10.1016/j.apnum.2018.10.014

M3 - 文章

AN - SCOPUS:85056273170

SN - 0168-9274

VL - 136

SP - 279

EP - 292

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

A kind of product integration scheme for solving fractional ordinary differential equations

Abstract

Keywords

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