Numerical solution of fractional differential equations by semiorthogonal B-spline wavelets

Can Liu; Xinming Zhang; Boying Wu

doi:10.1002/mma.5828

Numerical solution of fractional differential equations by semiorthogonal B-spline wavelets

Can Liu
, Xinming Zhang^*
, Boying Wu^*

^*Corresponding author for this work

Harbin Institute of Technology
School of Mathematics, Harbin Institute of Technology

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

7 Scopus citations

Abstract

In this paper, semiorthogonal B-spline wavelets collection method (SOBWCM) is applied for solving the fractional differential equations with derivatives in Caputo sense. This method transforms the original fractional differential equations to a system of algebraic equations based on the semiorthogonal B-spline wavelets and the relevant scaling functions on a bounded interval. The operational matrix of SOBWCM is presented, and the error analysis is derived. Finally, some test examples are provided to demonstrate the accuracy of the method.

Original language	English
Pages (from-to)	2697-2710
Number of pages	14
Journal	Mathematical Methods in the Applied Sciences
Volume	44
Issue number	4
DOIs	https://doi.org/10.1002/mma.5828
State	Published - 15 Mar 2021
Externally published	Yes

Keywords

Caputo derivatives
error analysis
operational matrix
semiorthogonal B-spline wavelets

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10.1002/mma.5828

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title = "Numerical solution of fractional differential equations by semiorthogonal B-spline wavelets",

abstract = "In this paper, semiorthogonal B-spline wavelets collection method (SOBWCM) is applied for solving the fractional differential equations with derivatives in Caputo sense. This method transforms the original fractional differential equations to a system of algebraic equations based on the semiorthogonal B-spline wavelets and the relevant scaling functions on a bounded interval. The operational matrix of SOBWCM is presented, and the error analysis is derived. Finally, some test examples are provided to demonstrate the accuracy of the method.",

keywords = "Caputo derivatives, error analysis, operational matrix, semiorthogonal B-spline wavelets",

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AU - Zhang, Xinming

AU - Wu, Boying

PY - 2021/3/15

Y1 - 2021/3/15

N2 - In this paper, semiorthogonal B-spline wavelets collection method (SOBWCM) is applied for solving the fractional differential equations with derivatives in Caputo sense. This method transforms the original fractional differential equations to a system of algebraic equations based on the semiorthogonal B-spline wavelets and the relevant scaling functions on a bounded interval. The operational matrix of SOBWCM is presented, and the error analysis is derived. Finally, some test examples are provided to demonstrate the accuracy of the method.

AB - In this paper, semiorthogonal B-spline wavelets collection method (SOBWCM) is applied for solving the fractional differential equations with derivatives in Caputo sense. This method transforms the original fractional differential equations to a system of algebraic equations based on the semiorthogonal B-spline wavelets and the relevant scaling functions on a bounded interval. The operational matrix of SOBWCM is presented, and the error analysis is derived. Finally, some test examples are provided to demonstrate the accuracy of the method.

KW - Caputo derivatives

KW - error analysis

KW - operational matrix

KW - semiorthogonal B-spline wavelets

UR - https://www.scopus.com/pages/publications/85076417430

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M3 - 文章

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 4

ER -

Numerical solution of fractional differential equations by semiorthogonal B-spline wavelets

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Keywords

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