Treatment for High-Order Linear Fredholm Integro-Differential Equations of Degenerated Kernel

In this work, projection method with degenerated Kernel and its properties are used to solve linear Fredholm Integro-Differential integral equations (LFIDE). The kernel in the equation are degenerated and convert to matrix in which each equations are integrated over the interval [0, 1] to produce the elements for obtaining the Eigen value. It approaches linear Fredholm Integro-Differential equations in a manner that gives the solution in an exact form and not in a series form, the algorithm is simple and effective, and could also provide an accurate approximate solution.