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Numerical solution of the Bagley–Torvik equation using shifted Chebyshev operational matrix
- Source :
- Advances in Difference Equations, Vol 2020, Iss 1, Pp 1-14 (2020)
- Publication Year :
- 2020
- Publisher :
- SpringerOpen, 2020.
-
Abstract
- In this study, an efficient numerical scheme based on shifted Chebyshev polynomials is established to obtain numerical solutions of the Bagley–Torvik equation. We first derive the shifted Chebyshev operational matrix of fractional derivative. Then, by the use of these operational matrices, we reduce the corresponding fractional order differential equation to a system of algebraic equations, which can be solved numerically by Newton’s method. Furthermore, the maximum absolute error is obtained through error analysis. Finally, numerical examples are presented to validate our theoretical analysis.
- Subjects :
- Chebyshev polynomials
Algebra and Number Theory
Partial differential equation
Differential equation
Applied Mathematics
lcsh:Mathematics
010102 general mathematics
lcsh:QA1-939
01 natural sciences
Chebyshev filter
010305 fluids & plasmas
Fractional calculus
Algebraic equation
Liouville–Caputo derivative
Approximation error
Ordinary differential equation
0103 physical sciences
Applied mathematics
0101 mathematics
Analysis
Bagley–Torvik equation
Collocation method
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 16871847
- Volume :
- 2020
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Advances in Difference Equations
- Accession number :
- edsair.doi.dedup.....7823a7c859fc1c1bd332fa42efc99357