(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Integral equations are essential in numerous domains of practical mathematics. This article introduces a straightforward, precise, and efficient iterative technique for resolving one-dimensional Fredholm integral equations of the second class. The suggested numerical method relies on Legendre wavelet functions. Utilizing these wavelets, the integral equation system is converted into a duo of interconnected systems of algebraic matrix equations. A finite iterative approach is employed to resolve these systems and ascertain the coefficients that formulate the approximate numerical solutions of the unknown functions. A variety of examples are included to evaluate the proposed numerical approach.