A Combination of Bernstein and Improved Block-Pulse Functions for Solving a System of Linear Fredholm Integral Equations

Author:

He Ji-Huan123ORCID,Taha Mahmoud H.4,Ramadan Mohamed A.5ORCID,Moatimid Galal M.4

Affiliation:

1. School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China

2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

3. National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, ChinaSoochow University, 199 Ren-Ai Road, Suzhou 215006, China

4. Department of Mathematics, Faculty of Education, Ain Shams University, Roxy 11566, Cairo, Egypt

5. Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia, 12946, Egypt

Abstract

The present paper illustrates a new numerical technique to solve a system of linear Fredholm integral equations of the second kind. The current work introduces a coupling between hybrid Bernstein functions and improved block-pulse functions (HBI). The current method transforms the linear second kind Fredholm integral equations system into an algebraic system that can be solved by using classical methods. Some numerical examples are introduced to validate the new approach. The results showed that the method is promising, powerful, ultimately accurate, and highly efficient.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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