Scientia Iranica

Scientia Iranica

Volume 19, Issue 6, December 2012, Pages 1691-1698
Scientia Iranica

An operational approach with Pade approximant for the numerical solution of non-linear Fredholm integro-differential equations

https://doi.org/10.1016/j.scient.2012.10.038Get rights and content
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Abstract

In this paper we extend the operational Adomian–Tau method with Pade approximant for the numerical solution of non-linear Fredholm integro-differential equations. To this end, we will present our method based on two simple matrices. Then unknown solution of the considered equation will be determined by using computational aspects of these matrices. Also we will use Pade approximant to improve accuracy of the method. Finally we demonstrate the method by numerical examples.

Keywords

Adomian–Tau method
Fredholm integro-differential equations
Matrix forms
Numerical solutions
Pade approximate solution

Cited by (0)

Ali Khani was born in Tabriz, Iran in 1968. He finished high school in 1988 and received his B.S. degree in Pure Mathematics and his M.S. degree in Applied Mathematics from University of Tabriz in 1993 and 1995, respectively. In 1996, he began working on the academic staff of the Azarbaijan University of Tarbiat Moallem in Iran. Dr. Khani was accepted for Ph.D studies in 2003, under the supervision of Professor Mahmoud Mohseni Moghadam, and received his degree in 2007 from Shahid Bahonar University of Kerman, Iran. He is presently an instructor of Applied Mathematics at Azarbaijan Shahid Madani University in Iran.

Sedaghat Shahmorad was born in Ardabil, Iran, in 1970 and finished high school in 1988. He subsequently received his B.S. and M.S. degrees in Mathematics and Applied Mathematics from University of Tabriz in 1993 and 1995, respectively. In 1996, he was accepted for Ph.D. studies at Tarbiat Modares University in Tehran, under the supervision of Professor Sayeed Mohammad Hosseini, receiving his Doctoral Degree in 2002. He is presently an instructor of Applied Mathematics at University of Tabriz in Iran.

Peer review under responsibility of Sharif University of Technology.

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This research has been supported by the Azarbaijan Shahid Madani University.