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

JiHuan He | Zendy; Mahmoud H. Taha | Zendy; Mohamed A. Ramadan | Zendy; Galal M. Moatimid | Zendy

Open Access

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

Author(s) -

JiHuan He,

Mahmoud H. Taha,

Mohamed A. Ramadan,

Galal M. Moatimid

Publication year - 2022

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2022/6870751

Subject(s) - fredholm integral equation , integral equation , algebraic equation , mathematics , fredholm theory , block (permutation group theory) , current (fluid) , system of linear equations , work (physics) , bernstein polynomial , coupling (piping) , integral transform , mathematical analysis , nonlinear system , physics , geometry , engineering , mechanical engineering , quantum mechanics , thermodynamics

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.

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