scholarly journals Series Solution for Single and System of Non-linear Volterra Integral Equations

2020 ◽  
Vol 4 (2) ◽  
pp. 6-8
Author(s):  
Narmeen N. Nadir
Keyword(s):  
Exact Solution ◽  
Integral Equations ◽  
Taylor Expansion ◽  
Series Solution ◽  
Volterra Integral Equations ◽  
Non Linear ◽  
Linear Volterra Integral Equations

In this paper, Taylor expansion has been used for solving non-linear Volterra integral equations (VIEs) of the second kind. This method allows us to overcome the difficulty caused by integrals and non-linearity; also, it has more precise and rapidly convergent to the exact solution. Two examples are presented for illustrate the performance of this method.

scholarly journals A Numerical Scheme to Solve Fuzzy Linear Volterra Integral Equations System

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
A. Jafarian ◽  
S. Measoomy Nia ◽  
S. Tavan
Keyword(s):  
Exact Solution ◽  
Integral Equations ◽  
Fuzzy System ◽  
Numerical Scheme ◽  
Taylor Expansion ◽  
Expansion Method ◽  
Volterra Integral Equations ◽  
Taylor Coefficients ◽  
Linear Volterra Integral Equations ◽  
The Given

The current research attempts to offer a new method for solving fuzzy linear Volterra integral equations system. This method converts the given fuzzy system into a linear system in crisp case by using the Taylor expansion method. Now the solution of this system yields the unknown Taylor coefficients of the solution functions. The proposed method is illustrated by an example and also results are compared with the exact solution by using computer simulations.

On a class of Volterra and Fredholm non-linear integral equations

1976 ◽  
Vol 79 (2) ◽  
pp. 329-335 ◽  
Author(s):  
P. J. Bushell
Keyword(s):  
Integral Equations ◽  
Kernel Function ◽  
Existence And Uniqueness ◽  
Volterra Integral Equations ◽  
Fredholm Equations ◽  
Non Linear ◽  
Linear Volterra Integral Equations ◽  
Linear Integral ◽  
Image Position ◽  
Linear Integral Equations

This paper concerns the existence and uniqueness of non-negative solutions of non-linear Volterra integral equations of the typeandwhere the kernel function k(.,.) is non-negative and sufficiently smooth, and either 0 < p < 1 or – 1 < p < 1. We will consider also the corresponding Fredholm equationsand

scholarly journals Deriving the Composite Simpson Rule by Using Bernstein Polynomials for Solving Volterra Integral Equations

2014 ◽  
Vol 11 (3) ◽  
pp. 1274-1281 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Exact Solution ◽  
Integral Equations ◽  
Bernstein Polynomials ◽  
Volterra Integral Equations ◽  
One Dimensional ◽  
Linear Volterra Integral Equations

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

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