In this paper, numerical solution of the linear second kind Fredholm integral equations is studied. These integral equations are widely used for solving many problems in mathematical physics and engineering. A new hybrid Bernstein and Improved Block-Pulse Functions ($\mathit{HBIBP}$) method is introduced and utilized to convert linear (nonlinear) second kind Fredholm integral equations into an algebraic equation. The new methodology is a combination of Bernstein polynomials (BPs) and improved block-pulse functions (IBPFs) on the interval [0, 1). Convergence analysis and numerical examples that illustrate the pertinent features of the method are presented.

中文翻译：

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一种新的正交正交伯恩斯坦混合算子和改进的块脉冲函数方法，用于解决数学物理和工程问题

本文研究了第二类线性Fredholm积分方程的数值解。这些积分方程被广泛用于解决数学物理学和工程学中的许多问题。新的混合Bernstein和改进的块脉冲函数（$\mathit{血压指数}$引入并利用）方法将线性（非线性）第二类Fredholm积分方程转换为代数方程。新的方法是在间隔[0，1）上结合了伯恩斯坦多项式（BP）和改进的块脉冲函数（IBPF）。给出了收敛性分析和数值示例，说明了该方法的相关功能。