In this paper, the multi-step differential transform method (MDTM), one of the most
effective method, is implemented to compute an approximate solution of the system of
nonlinear differential equations governing the problem. It has been attempted to show
the reliability and performance of the MDTM in comparison with the numerical method
(fourth-order Runge–Kutta) and other analytical methods such as HPM, HAM and DTM
in solving this problem. The first differential equation is the plane Couette flow equation
which serves as a useful model for many interesting problems in engineering. The second
one is the Fully-developed plane Poiseuille flow equation and finally the third one is the
plane Couette–Poiseuille flow.
