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 (Q1986183)

The author develops and implements a very interesting fourth-order numerical method - a nonuniform mesh optimal cubic B-spline collocation method - for the numerical solution of a strongly nonlinear singular boundary value problem. This method consists of five steps: \begin{itemize} \item L'Hôpital's rule is used to overcome the singularity behavior at the point \(r = 0\). \item Newton's method is used to linearize the resulting problem obtained in step 1. \item A grading function is appropriately chosen in order to generate a nonuniform partition over the solution domain. \item Cubic B-spline basis functions on nonuniform partition are constructed. \item An optimal B-spline collocation method on nonuniform mesh is designed to approximate the solution of the considered problem using the basis functions obtained in the previous step. \end{itemize} The convergence analysis of the proposed method is discussed.