A fourth-order non-uniform mesh optimal B-spline collocation method for solving a strongly nonlinear singular boundary value problem describing electrohydrodynamic flow of a fluid

Abstract

In this paper, a non-uniform mesh optimal B-spline collocation method is presented for the numerical solution of a singular two-point boundary value problem describing electrohydrodynamic flow (EF) of a fluid in a circular cylindrical conduit. The EF problem is highly nonlinear and has a singularity at the point r=0. Further, this problem has a boundary layer near right end of the solution domain. We consider a grading function to construct a non-uniform mesh over the problem domain. The non-uniform mesh is constructed in such a way that the mesh is finer near the right end boundary. Convergence of the proposed method is analyzed. The EF problem is solved for small and large values of the two relevant parameters: (i) strength of non-linearity β, and (ii) Hartmann electric number H. The effects of β and H on the velocity field are investigated. The computed results have been compared with those obtained by two other B-spline collocation methods over uniform mesh to show the advantage of the present method. It is shown that the present method provides O(h4) convergent approximation.