Dual solutions for the problem of mixed convection flow through a porous medium using an iterative finite difference method

The aim of this article is to approximate the multiple solutions of the problem of mixed convection in a porous medium on the half-line utilizing the quasilinearization method (QLM) combined with the finite difference method (FDM). For this purpose, at first, we transform the governing nonlinear differential equation to a sequence of linear differential equations via the quasilinearization approach. Then, we provide a sequence of linear algebraic systems by applying the FDM at each iteration to find the approximate solutions of the obtained linear differential equations. Moreover, we present a beneficial scheme to obtain appropriate initial guesses in order to compute both solutions of the problem. The convergence analysis is considered in detail and some numerical results are reported to demonstrate the validity of the proposed iterative method.