Adomian Decomposition Method Applied to Study Nonlinear Equations Arising in non-Newtonian flows

Adomian’s decomposition method (ADM) is employed to solve nonlinear differential equations which arise in non-Newtonian fluid dynamics. We study basic pipe flow problems of a third grade and 6-constant Oldroyd non-Newtonian fluids. The technique of Adomian decomposition is applied with elegant results. The solutions obtained show the reliability and efficiency of this analytical method. Numerical solutions are also obtained by solving nonlinear ordinary differential equations using Chebyshev spectral method. We present a comparative study of the analytical and numerical solutions. The analytical results agree well with the numerical results, which reveal the effectiveness and convenience of the Adomian decomposition method.