Computational Methods for Solving System of Volterra Integral Equation: Computational Methods for Solving System of linear Volterra Integral and Integro-differential Equations

K. Saeed, Rostam, M. Al-Faour, Omer

ISBN 10: 3844330755 / ISBN 13: 9783844330755

Published by LAP LAMBERT Academic Publishing, 2011

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Bibliographic Details

• Title: Computational Methods for Solving System of Volterra Integral Equation: Computational Methods for Solving System of linear Volterra Integral and Integro-differential Equations
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2011
• Language: English
• ISBN 10: 3844330755
• ISBN 13: 9783844330755
• Binding: Paperback
• Condition: Like New
• Book Type: book

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Synopsis

In this work the existence and uniqueness theorem for single linear Volterra integral equation has been generalized to a system of linear Volterra integral equation of the second kind. Depending on Banach fixed point theorem, some new results have been proved.Also, a Taylor series expansion has been considered to solve a system of linear Volterra integral equations of the second kind and a system of linear Volterra integro-differential equations of the second kind.In addition, three different types of iterative methods have been formulated to solve above systems. Furthermore, we derive a new iterative method named by "modified successive approximation method" to solve above systems. By this modification a faster rate of convergence for the successive method is established. Also, we proved a new theorem about the existence, uniqueness and convergence of this method. Two different kinds of weighted residual methods have been applied to treat the above systems. Moreover, the spectral method has been modified and applied for solving the above systems.

About the Author

Name: Dr. Rostam K. Saeed Place of Birth: Iraqi Kurdistan Region, Erbil. Scientific Rank: Professor E-mail: rostamkarim@yahoo.com, rostamkarim64@uni-sci.org