Perturbation–iteration solution for a third–grade fluid flowing between parallel plates

In this study, the perturbation-iteration algorithm is applied to two different 2D flows of third grade fluids between parallel plates. Primarily, two different perturbation-iteration algorithms depending on the perturbation correction terms and Taylor series expansion terms are developed for second-order ordinary differential equations and second-order coupled ordinary differential equations. The obtained algorithms are employed to the flow of a third grade non-Newtonian fluid between parallel plates and the flow of a Newtonian fluid between parallel plates with a Reynolds model viscosity. The solutions are contrasted with the numerical and regular perturbation solutions. Then the results found are discussed on graphs. It is found that the perturbation-iteration solutions converge better to the numerical solutions when compared with the regular perturbation solutions.