Approximate Analytical Solution of a Power-Law Pseudoplastic Fluid in a Boundary Layer over a Porous Plate: A New Application of Multi-Stage Parker-Sochacki Method

In this paper, based on Parker-Sochacki method for solving a system of differential equations, a multistage technique is developed for solving the nonlinear boundary layer equations of powerlaw fluid on infinite domain. The problem domain is split into subintervals over which the boundary value problem is replaced with a sequence of subproblems. In a shooting-like approach, the boundary condition at infinity is converted to an equivalent initial condition. By recasting the problem as a polynomial system of first-order autonomous equations, the sub-problems are solved with ParkerSochacki method with very high accuracy. The interval of convergence of the solution is derived a-priorly in terms of the parameters of the polynomial system, which guides optimal choice of the discretization parameter. The technique yielded a convergent piecewise continuous solution over the problem domain. The results obtained, demonstrated graphically and in tables, compared well with existing ones in the literature.