Selected Single-Step Hybrid Block Formula for Solving Third Order Ordinary Differential Equations With Application in Thin Film Flow

Abstract

This research paper examines the derivation of selected hybrid single-step block method for the numerical integration of third order ordinary differential equations. The method has the advantage of selecting only odd off-grid points within the interval of interest. The basis function for the formula is interpolated at three selected non-grid points within a single-step interval and collocated at all points. Further analysis of the basic numerical properties were established. The method was found to be A-stable, zero-stable and consistent. The small scale errors observed from numerical experiment indicate that the derived formula has better numerical approximations than some comparable methods in literature, while its application on practical thin film flow problem also showed improved solutions.