A novel approach for the numerical solution of nonlinear Fredholm integral equations using the Hosoya polynomial method

In this paper, we study the graph theoretical polynomial known as the Hosoya polynomial obtained from one of the standard classes of graphs called path. Using this polynomial applied for the numerical solution of the nonlinear Fredholm integral equation, which reduces in the algebraic system of equation with collocation points and then solving this system using Newton’s iterative with the help of MATLAB, we obtain the required approximate solution. The desired results are in terms of a set of continuous polynomials over a closed interval [0,1]. Illustrative applications show the efficiency, accuracy and validity of the proposed technique.