A Method Employing Legendre Wavelets and a Finite Iterative Approach for Efficiently Solving Systems of Linear Fredholm Integral Equations
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.6725Keywords:
Fredholm integral equations of the second kind, One-dimensional integral systems, Legendre wavelets, Iterative methods, numerical approximation, matrix equations, wavelet-based methodsAbstract
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.
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Copyright (c) 2025 Mohamed A. Ramadan , Mohamed Adel, Heba M. Arafa
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