A Hybrid Numerical Method Combining Legendre Polynomials and Improved Block-Pulse Functions for Solving Linear Systems of Fredholm Integral Equations

In order to solve linear systems of Fredholm integral equations, this paper proposes a novel hybrid numerical method that combines improved block-pulse functions with Legendre polynomials. By utilizing the orthogonality and strong approximation properties of Legendre polynomials along with the computational simplicity of improved block-pulse functions, the suggested method converts the integral system into an equivalent system of algebraic equations. The approach outperforms a number of conventional numerical methods in terms of accuracy and convergence speed. The robustness, efficiency, and stability of the suggested scheme are validated by several numerical remarks, which also show how well it works for solving complex Fredholm integral systems that arise in scientific and engineering applications.