Enactment of implicit two-step Obrechkoff-type block method on unsteady sedimentation analysis of spherical particles in Newtonian fluid media

The analysis of the characteristics of particles motion is considered in this article, where a model which studies a Newtonian fluid media with specific interest on the analysis of unsteady sedimentation of particles is considered. The numerical solution of this first order differential equation model using an Obrechkoff-type block method is presented. The algorithm for the conventional Nyström -type multistep scheme is considered with specific parameter choices in order to obtain the main k-step Obrechkoff-type block method and the required additional method. The unknown coefficients of these methods are obtained by using the concept of Taylor series expansion to obtain the required schemes for the block method which were combined as simultaneous integrators for the solution of the differential equation model. The block method gave highly accurate results as compared with the exact solution of the model. Furthermore, at selected values of the physical properties of nanoparticles, the solutions using the two-step Obrechkoff-type block method was compared with past literatures and the results were seen to be in agreement. The influence of the physical parameters on terminal velocity is also discussed. •The two-step Obrechkoff-type block method reduced the computational.•The accuracy of the block method is observed in comparison with the exact solution.•This method is recommended as approximation for first order differential equation.