Numerical Solution of Volterra-Fredholm Integral Equations Using Hybrid Orthonormal Bernstein and Block-Pulse Functions

2017 ◽  
Vol 4 (4) ◽  
pp. 1-14 ◽  
Author(s):  
Mohamed Ramadan ◽  
Mohamed Ali
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Fredholm Integral Equations ◽  
Block Pulse Functions

scholarly journals Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid Functions and the Collocation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Jianhua Hou ◽  
Beibo Qin ◽  
Changqing Yang
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Taylor Series ◽  
Fredholm Integral Equations ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Hybrid Function ◽  
Nonlinear Fredholm Integral Equations

A numerical method to solve nonlinear Fredholm integral equations of second kind is presented in this work. The method is based upon hybrid function approximate. The properties of hybrid of block-pulse functions and Taylor series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of algebraic equations. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

scholarly journals NUMERICAL SOLUTION OF MIXED LINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS BY MODIFIED BLOCK PULSE FUNCTIONS

2021 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
Ayyubi Ahmad
Keyword(s):  
Linear System ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Operational Matrix ◽  
Fredholm Integral Equations ◽  
Algebraic Equations ◽  
Block Pulse Functions ◽  
Operational Matrix Of Integration ◽  
Modified Block

A numerical method based on modified block pulse functions is proposed for solving the mixed linear Volterra-Fredholm integral equations. We obtain an integration operational matrix of modified block pulse functions on interval [0,T). A modified block pulse functions and their operational matrix of integration, the mixed linear Volterra-Fredholm integral equations can be reduced to a linear system of algebraic equations. The rate of convergence is O(h) and error analysis of the proposed method are discussed. Some examples are provided to show that the proposed method have a good degree of accuracy.

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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