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Research Article Open access CC BY 4.0

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

Mohamed A. Ramadan, Mohamed R. Ali

Asian Research Journal of Mathematics · pp. 1–14 · Published 25 Jun 2017

10.9734/ARJOM/2017/34324

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 Block-Pulse 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.

Hybrid orthonormal Bernstein and Block-Pulse functions linear Volterra-Fredholm integral equations integration of the cross product product matrix coefficient matrix

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