Newton–Tau Method

Many applied problems have their natural mathematical setting as integral and integro-differential equations, thus they usually have the advantage of simpler methods of solution. In addition, a large class of initial and boundary value problems, associated with differential equations, can be reduced to integral equations. Problems in human population, mortality of equipment and its rate of replacement, biological species living together, torsion of a wire, automatic control of a rotating shaft, radiation transport and determining the energy spectrum of neutrons, and electromagnetic fields [1] are some of the fields that are integral and integro-differential equations. Many numerical and analytic methods for solving integral and integro-differential equations exist but few of them are for solving nonlinear equations. Tau’s method is used for solving integral and differential equations [2–5]. Here we combine the Newton’s method and Tau’s method for solving nonlinear Fredholm integral and integro-differential equations.