scholarly journals A Jacobi-Collocation Method for Second Kind Volterra Integral Equations with a Smooth Kernel

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hongfeng Guo ◽  
Haotao Cai ◽  
Xin Zhang
Keyword(s):  
Integral Operator ◽  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations ◽  
Numerical Example ◽  
Fully Discrete ◽  
Smooth Kernel ◽  
Jacobi Collocation Method

The purpose of this paper is to provide a Jacobi-collocation method for solving second kind Volterra integral equations with a smooth kernel. This method leads to a fully discrete integral operator. First, it is shown that the fully discrete integral operator is stable in bothL∞and weightedL2norms. Then, the proposed approach is proved to arrive at an optimal (the most possible) convergent order in both norms. One numerical example demonstrates the efficiency and accuracy of the proposed method.

Collocation method for Fredholm and Volterra integral equations

Kybernetes ◽  
2013 ◽  
Vol 42 (3) ◽  
pp. 400-412 ◽  
Author(s):  
Jalil Rashidinia ◽  
Zahra Mahmoodi
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations

scholarly journals A New Neumann Series Method for Solving a Family of Local Fractional Fredholm and Volterra Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-Jing Ma ◽  
H. M. Srivastava ◽  
Dumitru Baleanu ◽  
Xiao-Jun Yang
Keyword(s):  
Integral Operator ◽  
Integral Equations ◽  
Fractional Integral ◽  
Neumann Series ◽  
Volterra Integral Equations ◽  
Fractional Integral Operator ◽  
Series Method ◽  
Operator Type ◽  
Local Fractional Integral

We propose a new Neumann series method to solve a family of local fractional Fredholm and Volterra integral equations. The integral operator, which is used in our investigation, is of the local fractional integral operator type. Two illustrative examples show the accuracy and the reliability of the obtained results.

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