On the Modified Block-Pulse Function for Volterra Integral Equation of The First Kind
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
M. Mohammadi
1
(Department of Mathematics, South Tehran Branch, Islamic Azad university, Tehran, Iran.)
A. R. Vahidi
2
(Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran.)
T. Damercheli
3
(Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran.)
S. Khezerloo
4
(Department of Mathematics, South Tehran Branch, Islamic Azad university, Tehran, Iran.)
M. Nouri
5
(Department of Mathematics, South Tehran Branch, Islamic Azad university, Tehran, Iran.)
کلید واژه: Volterra integral equation of the first kind, Block-pulse functions, Operational matrix, Function expansion, Convergence,
چکیده مقاله :
In this paper, we consider Volterra integral equations of the first kind. Then by extending the modified Block-pulse functions(MBPFs) on the Volterra integral equation of the second kind obtained from Volterra integral equation of the first kind, we obtain the approximate solution. Some theorems are proved to provide an error analysis for proposed method. Numerical examples show that the proposed scheme has a suitable degree of accuracy.
In this work, we present a simple efficient modified Block-Pulse functions (MBPFs) for numerical solution of class of linear Volterra integral equation of first kind. The peresent method is based on converting Volterra integral equation of the first kind into Volterra integral equation of the second kind. Some theorems are included to show the convergence and advantage of this method. Numerical results show that the approximate solutions have a good degree of ‎accuracy.‎
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