### Abstract

Chebyshev polynomials are utilized to obtain solutions of a set of p th order linear differential equations with periodic coefficients. For this purpose, the operational matrix of differentiation associated with the shifted Chebyshev polynomials of the first kind is derived. Utilizing the properties of this matrix, the solution of a system of differential equations can be found by solving a set of linear algebraic equations without constructing the equivalent integral equations. The Floquet Transition Matrix (FTM) can then be computed and its eigenvalues (Floquet multipliers) subsequently analyzed for stability. Two straightforward methods, the differential state space formulation and the differential direct formulation, are presented and the results are compared with those obtained from other available techniques. The well-known Mathieu equation and a higher order system are used as illustrative examples.

Original language | English (US) |
---|---|

Pages (from-to) | 165-190 |

Number of pages | 26 |

Journal | Mathematical Problems in Engineering |

Volume | 2 |

Issue number | 2 |

DOIs | |

State | Published - 1996 |

Externally published | Yes |

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### Keywords

- Differentiation operational matrix
- Floquest transition matrix(FTM)
- Floquet multiplier
- Periodic systems
- Shifted Chebyshev palynomials of the first kind
- Stability

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

### Cite this

**Solution and stability of a set of PTH order linear differential equations with periodic coefficients via Chebyshev polynomials.** / Sinha, S. C.; Butcher, Eric.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Solution and stability of a set of PTH order linear differential equations with periodic coefficients via Chebyshev polynomials

AU - Sinha, S. C.

AU - Butcher, Eric

PY - 1996

Y1 - 1996

N2 - Chebyshev polynomials are utilized to obtain solutions of a set of p th order linear differential equations with periodic coefficients. For this purpose, the operational matrix of differentiation associated with the shifted Chebyshev polynomials of the first kind is derived. Utilizing the properties of this matrix, the solution of a system of differential equations can be found by solving a set of linear algebraic equations without constructing the equivalent integral equations. The Floquet Transition Matrix (FTM) can then be computed and its eigenvalues (Floquet multipliers) subsequently analyzed for stability. Two straightforward methods, the differential state space formulation and the differential direct formulation, are presented and the results are compared with those obtained from other available techniques. The well-known Mathieu equation and a higher order system are used as illustrative examples.

AB - Chebyshev polynomials are utilized to obtain solutions of a set of p th order linear differential equations with periodic coefficients. For this purpose, the operational matrix of differentiation associated with the shifted Chebyshev polynomials of the first kind is derived. Utilizing the properties of this matrix, the solution of a system of differential equations can be found by solving a set of linear algebraic equations without constructing the equivalent integral equations. The Floquet Transition Matrix (FTM) can then be computed and its eigenvalues (Floquet multipliers) subsequently analyzed for stability. Two straightforward methods, the differential state space formulation and the differential direct formulation, are presented and the results are compared with those obtained from other available techniques. The well-known Mathieu equation and a higher order system are used as illustrative examples.

KW - Differentiation operational matrix

KW - Floquest transition matrix(FTM)

KW - Floquet multiplier

KW - Periodic systems

KW - Shifted Chebyshev palynomials of the first kind

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=0041632516&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041632516&partnerID=8YFLogxK

U2 - 10.1155/S1024123X96000294

DO - 10.1155/S1024123X96000294

M3 - Article

AN - SCOPUS:0041632516

VL - 2

SP - 165

EP - 190

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

IS - 2

ER -