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

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.