A Method Employing Legendre Wavelets and a Finite Iterative Approach for Efficiently Solving Systems of Linear Fredholm Integral Equations (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.
Keywords: Fredholm integral equations of the second kind; One-dimensional integral systems; Legendre wavelets; Iterative methods; numerical approximation; matrix equations; wavelet-based methods