A new iterative algorithm for a strongly nonlinear singular boundary value problem

Abstract

Recently, Mastroberardino (2011) proposed a homotopy analysis method (HAM) for solving a nonlinear singular boundary value problem (SBVP) governing electrohydrodynamic flow (EHF) of a fluid in an ion drag configuration in a circular cylindrical conduit. The nonlinearity confronted in this problem is in the form of rational function. The HAM (Mastroberardino, 2011) produces a series solution to the problem, but requires a large number of iterations for obtaining a reasonable analytical approximation. In this paper, we propose a new iterative technique, namely the discrete optimized homotopy analysis method (DOHAM), based on a domain decomposition approach and an optimized HAM for solving the same problem. Convergence of the new method is carried out. The uniqueness of solution of the problem is established. Computational results reveal that our method provides better results as compared to some existing iterative methods. The velocity field of electrohydrodynamic flow of a fluid is computed. The influence of the strength of non-linearity and the Hartmann electric number on the velocity profile is investigated.