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

Asian Research Journal of Mathematics • 2017
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Publication Information
Authors Mohamed R. Ali
Keywords Hybrid orthonormal Bernstein and Block-Pulse functions; linear Volterra-Fredholm integral equations; integration of the cross product; product matrix; coefficient matrix.
Journal Asian Research Journal of Mathematics
Publisher Not Available
Volume 4
Issue 4
Pages 1-14
publication.type International
Paper Link Not Available
Supplementary Materials Not Available
Abstract
We have proposed an efficient numerical method to solve a class of mixed Volterra-Fredholm integral
equations (VFIE’s) of the second kind, numerically based on Hybrid Orthonormal Bernstein and BlockPulse
Functions
(OBH).
The
aim
of
this
paper
is
to
apply
OBH
method
to
obtain
approximate
solutions
of

nonlinear

Fuzzy Fredholm Integro-differential Equations. First we introduce properties of Hybrid
Orthonormal Bernstein and Block-Pulse Functions, we used it to transform the integral equations to
the system of linear algebraic equations then an iterative approach is proposed to obtain approximate
solution of class of linear algebraic equations, a numerical examples is presented to illustrate the
proposed method. The error estimates of the proposed method is given.