### Abstract

In this article, a general framework for solving system of ordinary differential equations by implementing a relatively new numerical technique called the Legendre operational matrix of differentiation is presented for the first time. This method can be an effective procedure to obtain analytic and approximate solutions for different systems of ordinary differential equations. Different from other numerical techniques, shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. Comparisons are made between approximate solutions, exact solutions and numerical ones for several examples. Moreover, estimate error for the given algorithm is presented.

Original language | English |
---|---|

Pages (from-to) | 483-494 |

Number of pages | 12 |

Journal | Italian Journal of Pure and Applied Mathematics |

Volume | 36 |

Publication status | Published - 2016 |

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### Keywords

- Legendre polynomials
- Operational matrix of differentiation
- System of ordinary dierential equations

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Italian Journal of Pure and Applied Mathematics*,

*36*, 483-494.

**On the approximate solutions of systems of odes by legendre operational matrix of differentiation.** / Bani-Ahmad, F.; Alomari, A. K.; Bataineh, A. Sami; Sulaiman, J.; Hashim, Ishak.

Research output: Contribution to journal › Article

*Italian Journal of Pure and Applied Mathematics*, vol. 36, pp. 483-494.

}

TY - JOUR

T1 - On the approximate solutions of systems of odes by legendre operational matrix of differentiation

AU - Bani-Ahmad, F.

AU - Alomari, A. K.

AU - Bataineh, A. Sami

AU - Sulaiman, J.

AU - Hashim, Ishak

PY - 2016

Y1 - 2016

N2 - In this article, a general framework for solving system of ordinary differential equations by implementing a relatively new numerical technique called the Legendre operational matrix of differentiation is presented for the first time. This method can be an effective procedure to obtain analytic and approximate solutions for different systems of ordinary differential equations. Different from other numerical techniques, shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. Comparisons are made between approximate solutions, exact solutions and numerical ones for several examples. Moreover, estimate error for the given algorithm is presented.

AB - In this article, a general framework for solving system of ordinary differential equations by implementing a relatively new numerical technique called the Legendre operational matrix of differentiation is presented for the first time. This method can be an effective procedure to obtain analytic and approximate solutions for different systems of ordinary differential equations. Different from other numerical techniques, shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. Comparisons are made between approximate solutions, exact solutions and numerical ones for several examples. Moreover, estimate error for the given algorithm is presented.

KW - Legendre polynomials

KW - Operational matrix of differentiation

KW - System of ordinary dierential equations

UR - http://www.scopus.com/inward/record.url?scp=84991085118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84991085118&partnerID=8YFLogxK

M3 - Article

VL - 36

SP - 483

EP - 494

JO - Italian Journal of Pure and Applied Mathematics

JF - Italian Journal of Pure and Applied Mathematics

SN - 1126-8042

ER -