Legendre Wavelets Direct Method for the Numerical Solution of Fredholm Integral Equation of the First Kind

In this paper, an efficient direct method based on Legendre wavelets is introduced to approximate the solution of Fredholm integral equations of the first kind. These basic functions are orthonormal and have compact support. The properties of the Legendre wavelets are utilized to convert the integral equations into a system of linear algebraic equations. The main characteristic of the method is low cost of setting up the equations without using any projection method. Furthermore an estimation of error bound for the present method is proved. Finally, some numerical examples are provided to demonstrate the applicability and accuracy of the proposed technique.