Solving Fredholm Integral Equation of the Second Kind with A Single Core

Integral equation with a single core has a special importance in different fields of science. Hence, in this article we have tried to obtain an estimation of a single core of integral equation by using correct method of sectioning a network of points. To this end, for obtaining a solution for integral equation, orthogonal base unit generated based on Legendre polynomials is used and the number of operations are reduced due to orthogonality of the above bases and operational matrixes are appeared as diagonal. In the end, obtained numerical results indicate to a high level of accuracy for the estimation.