Legendre Wavelets for Systems of Fredholm Integral Equations of the Second Kind

Orthogonal functions and polynomials have been used by many authors for solving various problems. The main idea of using orthogonal basis is that a problem reduces to solving a system of linear or nonlinear algebraic equations by truncated series of orthogonal basis functions for solution of problem and using the operational matrices. Here we use Legendre wavelets basis on interval [0, 1]. Some of its applications are nonlinear VolterraFredholm integral equation [2], Fredholm integral equations of the first kind [3], Abel’s integral equations [4], nonlinear integral equations [5], differential equations of Lane-Emden type [6], variational problems [7] and some other problems. Systems of Fredholm integral equations of the second kind have been solved by other methods as well, Adomian decomposition method [9], Taylor-series expansion method [10], Sinccollocation method [11], Homotopy perturbation method [12].