Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis-Reference-Cited by-同舟云学术

Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

Published:2014 Issue: Volume:2014 Page:1-8
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Alipour Mohsen¹^ORCID,Baleanu Dumitru²³⁴,Babaei Fereshteh¹

Affiliation:

1. Faculty of Basic Science, Babol University of Technology, P.O. Box 47148-71167, Babol, Iran

2. Department of Mathematics, Cankaya University, Ogretmenler Caddesi 14, Balgat, 06530 Ankara, Turkey

3. Institute of Space Sciences, P.O. Box MG 23, Magurele, 077125 Bucharest, Romania

4. Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia

Abstract

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/623763.pdf

Reference21 articles.

1. Direct method to solve Volterra integral equation of the first kind using operational matrix with block-pulse functions

2. Modification of Block Pulse Functions and their application to solve numerically Volterra integral equation of the first kind

3. Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions

4. Solution of nonlinear Volterra–Fredholm–Hammerstein integral equations via rationalized Haar functions

5. A composite collocation method for the nonlinear mixed Volterra–Fredholm–Hammerstein integral equations

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