scholarly journals Numerical solution of nonlinear Volterra–Fredholm–Hammerstein integral equations in two-dimensional spaces based on Block Pulse functions

2017 ◽  
Vol 317 ◽  
pp. 565-572 ◽  
Author(s):  
Jiaquan Xie ◽  
Qingxue Huang ◽  
Fuqiang Zhao
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Two Dimensional ◽  
Hammerstein Integral Equations ◽  
Block Pulse Functions

scholarly journals Numerical solution of two dimensional nonlinear fuzzy Fredholm integral equations of second kind using hybrid of block-pulse functions and Bernstein polynomials

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4923-4935 ◽  
Author(s):  
Vahid Mahaleh ◽  
Reza Ezzati
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Approximation Method ◽  
Numerical Stability ◽  
Bernstein Polynomials ◽  
Fredholm Integral Equations ◽  
Successive Approximation Method ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Block Pulse Functions

In this paper, first, we introduce a successive approximation method in terms of a combination of Bernstein polynomials and block-pulse functions. The proposed method is given for solving two dimensional nonlinear fuzzy Fredholm integral equations of the second kind. Then, we present the convergence of the proposed method. Also we investigate the numerical stability of the method with respect to the choice of the first iteration. Finally, two numerical examples are presented to show the accuracy of the method.

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