# Taylor Series Method for the System of Linear Volterra Integro-differential Equations

Volume 4, Issue 3, pp 331--343 Publication Date: April 15, 2012
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### Authors

J. Rashidinia - School of Mathematics, Iran University of Science and Technology, P. O. Box, 16846-13114, Tehran, Iran A. Tahmasebi - School of Mathematics, Iran University of Science and Technology, P. O. Box, 16846-13114, Tehran, Iran

### Abstract

A method to determine the numerical solution of system of linear Volterra integro-differential equations (IDEs) is proposed. The method obtains Taylor expansion for the exact solution of system of linear Volterra IDEs at initial point $x = 0$. In addition, we introduce a procedure to obtain an approximation for Taylor expansion of the exact solution at $x\neq 0$. Moreover, error estimation of the proposed methods is presented. The efficiency and applicability of the presented methods is illustrated by some numerical examples.

### Keywords

• system of linear Volterra integro-differential equations
• numerical solution
• Taylor expansion
• power series method
• integral equation.

•  65R20
•  45J05
•  68W30

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